Hong Kong Probability Seminar

Coordinators: Pierre Nolin (CityU), Jianfeng Yao (HKU)

Organizers:

Presentation

Probabilists in Hong Kong are much dispersed in several universities, and they had notable difficulty to meet regularly for fruitful exchanges. The Hong Kong Probability Seminar aims at filling this gap. Each month the seminar features two talks by experts in probability theory, as well as related fields. Each talk lasts for approximately 90 minutes: such extended lecture time, the informal style of the seminar, and a coffee break between talks should ease interactions among the participants.






Year 2018–2019


    • January 11, 2019 (HKU)        

      • 2:00–3:30pm: Ka Chun Cheung  (HKU):     On asymptotic additivity of tail risk measures

        Abstract:  As perceived from daily experience together with numerous empirical studies, upper tail comonotonicity adequately describes the extremal dependence structure of multivariate risks especially over the course of financial turmoils or industrial accidents and outbreaks. Under this dependence structure, we establish the .universal asymptotic additivity, as the probability level approaching to 1, for both Value-at-Risk and Conditional Tail Expectation for a portfolio of risks, in which each marginal risk could be any one having a finite endpoint or belonging to one of the three maximum domains of attraction. This covers most distributions commonly encountered in practice. Our results do not require the tail equivalence assumption as needed in the existing literature, and resolve a lasting problem in quantitative risk management. If time permits, results on asymptotic sub/super-additivity of tail risk measures under general Archimedean copula with regular varying generator will also be discussed.

        This talk is based on a joint work with Hok Kan Ling, Qihe Tang, Phillip Yam and Fei Lung Yuen.

      • 3:30–4:00pm: coffee break
      • 4:00–5:30pm: Zuoquan  Xu  (Poly U):  On probability distortion and applications in behavioral finance

        Abstract:  In this talk, I will first introduce probability distortion/weighting function and its roles in behavioral finance theories.  Then I will describe the recent development of the so-called quantile optimization method, a main tool to deal with optimization problems involving probability weighting from financial economics. In particular, portfolio selection, optimal stopping, and insurance models will be solved by this method.

Venue:  Room 301, Run Run Shaw Building, HKU   (The event is supported by the  Department of Statistics and Actuarial Science, The University of Hong Kong).
    • November 23, 2018 (HKUST)            Poster to print

      • 1:30–2:30pm: Rongfeng Sun (National University of Singapore)
        Moment asymptotics for the (2+1)-dimensional directed polymer in the critical window

        Abstract: The partition function of the directed polymer model on Z^{2+1} has been shown to undergo a phase transition on an intermediate disorder scale. In this talk, we focus on a window around the critical point. Exploiting a renewal process representation, we identify the asymptotics for the second and third moments of the partition function. As a corollary, we show that, viewed as a random field, the family of partition functions admits non-trivial diffusive scaling limits, and each limit point has the same covariance structure with logarithmic divergence near the diagonal. Similar results are obtained for the stochastic heat equation on R^2, extending earlier results by Bertini and Cancrini (98). Based on joint work with F. Caravenna and N. Zygouras.

        Venue: Room 2502, HKUST

      • 2:30–3:00pm: coffee break (Room 2502, HKUST)

      • 3:00–4:00pm: Tomohiro Sasamoto (Tokyo Institute of Technology)
        The Kardar-Parisi-Zhang (KPZ) models and their universality

        Abstract: The Kardar-Parisi-Zhang (KPZ) equation is a nonlinear stochastic partial differential equation which was introduced in 1986 to describe the motion of interface. Fluctuations of the interface exhibit universal scaling laws, now known as the KPZ universality. In 2010 the exact formula for the one-point height distribution was discovered by Sasamoto-Spohn and Amir-Corwin-Quastel and there have been many developments since then.
        In this talk, we start from explaining the basics about the KPZ equation and its universality. We first present the equation and discuss the issue of its well-definedness. Then we show and explain how to derive the exact formula for the height distribution, and study its limiting behaviors.
        Then we discuss various recent developments on the topic. They include the introduction and analysis of various lattice models in the KPZ universality, the connections to integrable systems and representation theory, and generalizations to multi-component systems. Finally we also mention a few outstanding problems on the subject.

        Venue: Lecture Theater F, HKUST      (This talk is joint with the departmental colloquium)

    • November 2, 2018 (CUHK)            Poster to print

      • 2:00–3:30pm: Jie Xiong (Southern University of Science and Technology)
        Stackelberg game with partial information

        Abstract: Motivated by the cooperative advertising and pricing problems, we consider the leader-follower game with asymmetric information. As preparation, I will first introduce the theory of nonlinear filtering which is one of the main tool used in this research. After that we consider the general stochastic maximum principles under partial information when the state is given by a BSDE or an FBSDE with or without mean-field term. After these preparation, we will discuss the stochastic game under asymmetric information structure.

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Chen Wang (HKU)
        Some new results on random matrix theory with application to analysis of dynamic factor models

        Abstract: This talk consists of two parts. In the first part, I will give a brief introduction to some relevant results of random matrix theory (RMT). The second part will focus on a specific application, that is, the order determination of large dimensional dynamic factor model.

      Venue:  LT1, Lady Shaw Building, CUHK      (The event is supported by the Department of Statistics, The Chinese University of Hong Kong).

    • October 5, 2018 (HKU)            Poster to print

      • 2:00–3:30pm: Phillip Yam (CUHK)
        Beyond classical portfolio selection

        Abstract: Since the first introduction in Markowitz (1952), portfolio choice theory has been one of the key research topics in mathematical finance, and it is a formal one on striving for an ideal balance between the portfolio return and reducing its inherent risk inherited from various financial markets and operations. Yet, with the increasing sophistication of different markets, even in the presence of notable behavioral bias of investors, there is an urgent call for reframing the landscape of this traditional research area in response to new desire. Based on some of my recent research effort, I shall aim to share with my view on some possible new directions that can cater those practical considerations.

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Pierre Tarrès (NYU Shanghai)
        Self-interacting random walks and statistical physics

        Abstract: We start by a review of recent questions and results on self-interacting random walks. Then we explain how the Edge-reinforced random walk, introduced by Coppersmith and Diaconis in 1986, is related to several models in statistical physics, namely the supersymmetric hyperbolic sigma model studied by Disertori, Spencer and Zirnbauer (2010), the random Schrödinger operator and Dynkin's isomorphism.
        These correspondences enable us to show recurrence/transience results on the Edge-reinforced random walk, and they also allow us to provide insight into these models. This work is joint with Christophe Sabot, and part of it is also in collaboration with Margherita Disertori, Titus Lupu and Xiaolin Zeng.

      Venue:  Room 103, Run Run Shaw Building, HKU      (The event is supported by the Institute of Mathematical Research, Department of Mathematics, HKU).




    Year 2017–2018



    • April 27, 2018 (CUHK)            Poster to print

      • 2:00–3:30pm: Ke Wang (HKUST)
        Random perturbation of low-rank matrices and applications

        Abstract: Computing the singular values and singular vectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. It is naturable to understand the essential spectral parameters of this perturbed matrix, such as its spectral norm, the leading singular values, and vectors, or the subspace formed by the first few singular vectors. Classical (deterministic) theorems, such as those by Davis-Kahan, Wedin, and Weyl, give tight estimates for the worst-case scenario. In this talk, I will consider the case when the perturbation is random. In this setting, better estimates can be achieved when the data matrix has low rank. I will also discuss some applications of our results. This talk is based on joint works with Sean O'Rourke and Van Vu.

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Lihu Xu (University of Macau)
        Approximation of stable law in Wasserstein distance by Stein's method

        Abstract: We will first give a fast review of some preliminaries of stable law, stable processes, ergodicity of SDEs driven by stable noises, and then talk how to obtain the convergence rate of stable law in Wasserstein distance by Stein's method. If the time is permitted, we will give a sketch on using a method recently developed by Fang, Shao and Xu to sample high dimensional stable distribution by discretizing Ornstein-Uhlenbeck stable processes. This talk is based on the paper arXiv:1709.00805 and a joint work in progress with Peng Chen (PhD student at UM) and Ivan Nourdin (Luxembourg).

      Venue:  LT3, Lady Shaw Building, CUHK (The event is supported by the Department of Statistics, The Chinese University of Hong Kong).

    • March 23, 2018 (HKUST)         Poster to print

      • 2:00–3:30pm: Benoît Collins (Kyoto University)
        Strong convergence for random permutations

        Abstract: We consider an n dimensional random matrix model obtained from a non-commutative polynomial in d unitaries and their inverse, after replacing the formal unitaries by random iid permutation matrices. This model has an obvious (Perron Frobenius) eigenvector and leaves invariant its orthogonal. We study the large n limit behavior of this model on the orthogonal of the PF eigenvector and show that in addition to asymptotic freeness, it has asymptotically no outliers. Time allowing, we will also discuss applications to random graph theory.
        This is joint work with Charles Bordenave.

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Laurent Ménard (Université Paris Ouest Nanterre)
        Random planar triangulations with an Ising model

        Abstract: Angel and Schramm proved in 2003, that uniform planar triangulations converge for the local topology. The limit law, known as UIPT (for Uniform Infinite Planar Triangulation) has been much studied since and is now a well understood object.
        In this talk, I'll explain how such objects are defined and studied. In particular, I'll explain why the algebraicity of the generating functions is crucial, and where it comes from.
        I'll then turn to triangulations weighted by an Ising model and show how to extend the combinatorial results known for uniform triangulations and the local weak convergence.
        This is a joint work with Marie Albenque and Gilles Schaeffer.  

      Venue:  Room 4475 (via Lifts 25/26)​, Academic Building, HKUST.

    • March 2, 2018 (HKU)          Poster to print

      • 2:00–3:30pm: Tze Leung Lai (Stanford)
        MCMC with sequential state substitutions: theory and applications

        Abstract: Motivated by applications to adaptive filtering that involves joint parameter and state estimation in hidden Markov models, we describe a new approach to MCMC, which uses sequential state substitutions for its Metropolis-Hastings-type transitions. The basic idea is to approximate the target distribution by the empirical distribution of N representative atoms, chosen sequentially by an MCMC scheme so that the empirical distribution converges weakly to the target distribution as the number K of iterations approaches infinity. Making use of coupling arguments and bounds on the total variation norm of the difference between the target distribution and the empirical measure defined by the sample paths of the MCMC scheme, we develop its asymptotic theory. In particular, we establish the asymptotic normality (as both K and N become infinite) of the estimates of functionals of the target distribution using the new MCMC method, provide consistent estimates of their standard errors, and derive oracle properties that prove their asymptotic optimality. Implementation details and applications, particularly to adaptive particle filtering with consistent standard error estimate, are also given.

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Chung Yin Amy Pang (HKBU)
        Lumpings of algebraic Markov chains arise from subquotients

        Abstract: A function on the state space of a Markov chain is a “lumping” if observing only the function values gives a Markov chain. I will describe some classical examples of lumping, for some card-shuffling models, then explain how these lumpings can be proved in a uniform way through the framework of “algebraic Markov chains”. This talk is based on Part I of the preprint of the same title.  

      Venue:  Room 210, Run Run Shaw Building, HKU   (The event is supported by the Institute of Mathematical Research, Department of Mathematics, The University of Hong Kong).

    • January 26, 2018 (CityU)          Poster to print

      • 2:00–3:30pm: Xiao Fang (CUHK)
        An introduction to Stein’s method

        Abstract: Stein's method is a powerful tool for proving limit theorems along with error bounds. The method works for both normal and non-normal approximations for random variables with various dependency structures. In this talk, I will give a brief introduction to Stein's method. 

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Jianfeng Yao (HKU)
        On central limit theorems for eigenvalue statistics of a large Wigner matrix 

        Abstract: In this talk, I will first review some well established central limit theorems for eigenvalues of a large Wigner matrix. The focus will then be on a CLT given in Bai and Yao (Bernoulli, 2005) with a detailed description of the main tools and steps of its proof. In the second part of the talk, I will discuss a related problem we recently studied for the adjacency matrix of a large random graph from the so-called “stochastic block model”.

      Venue:  Yeung Kin Man Acad Building (Academic 1), Room Y5-305 (Yellow zone, 5th floor), CityU 

    • December 15, 2017 (HKUST)      Poster to print

      • 2:00–3:30pm: Guangyue Han (HKU)
        An introduction to information theory

        Abstract: In this talk, I will give a brief introduction to information theory and talk about some open problems and certain research directions.

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Xinghua Zheng (HKUST)
        Spatial SIR epidemic processes and their asymptotics

        Abstract: We focus on a special interacting particle system known as SIR epidemic model. We will discuss its connection with branching random walk (and percolation), its measure-valued limiting process at or near criticality, and the associated phase transition phenomena. The talk is  based on joint works with Steve Lalley, Ed Perkins and Eyal Neuman.

      Venue:  Lecture Theatre K (LTK), Academic Building, HKUST

    • November 17, 2017 (CUHK)         Poster to print

      • 2:00–3:00pm: István Berkes (TU Graz)
        Fluctuations of stochastic processes and strong invariance principles

        Abstract: Describing the fluctuations of stochastic processes over short intervals is a basic problem of probability theory with numerous applications in statistics. For example, to detect short term, "epidemic" changes in the structure of time series requires studying the fluctuations of the partial sum process of the sample (X1, X2, ... , Xn) over intervals of length very short compared with n. If X1, X2, ... are i.i.d. Gaussian variables, such results are available from the theory of Wiener process and using the celebrated Komlós-Major-Tusnády (KMT) approximation theorem, these results can be extended to the general i.i.d. case. For the case of weakly dependent sequences, a class covering many important applications, the KMT theorem is not available, except for a few special cases settled recently (Berkes-Liu-Wu 2014, Merlevède and Rio 2015). The purpose of this talk to show that using a simple modification of the elementary Bernstein blocking technique combined with the original KMT result, we can get widely applicable fluctuation results for many weakly dependent models, such as mixing processes, Markov processes, Gaussian processes, etc.

      • 3:00–3:30pm: coffee break

      • 3:30–5:00pm: Jian Song (HKU)
        Long-term asymptotics for (fractional) Anderson models

        Abstract: In this talk, I will review our recent results on the long-term behavior of the solutions to the parabolic and hyperbolic Anderson models. The talk will consist of two parts. The first part concerns the existence and uniqueness of the solutions to the (fractional) heat equation and wave equation driven by multiplicative Gaussian noise, and the Feynmnan-Kac formula for stochastic heat equation. The second part deals with moments Lyapunov exponents for the solutions to the (fractional) Anderson models.

      Venue:  LT9, Yasumoto international Academic Park (YIA), CUHK (The event is supported by the Department of Statistics, The Chinese University of Hong Kong).

    • October 20, 2017 (HKU)               Poster to print

      • 2:00–3:30pm: Pierre Nolin (CityU)
        Frozen percolation and self-organized criticality

        Abstract: We first give a short introduction to Bernoulli percolation, which is obtained by deleting at random, independently, the edges (or the vertices) of a given lattice. It is arguably one of the simplest models from statistical mechanics displaying a phase transition, i.e. a drastic change of macroscopic behavior, at a certain critical threshold. We present the main tools and techniques used to study percolation, as well as the most important results. We then discuss the frozen percolation model, where connected components stop growing ("freeze") as soon as they become large (i.e. reach a "size" at least N, for some finite parameter N). In particular, we explain why the "near-critical" regime of Bernoulli percolation arises. This talk is based on joint works with Rob van den Berg (CWI and VU, Amsterdam) and Demeter Kiss.

      • 3:30–4:00pm: coffee break

      • 4:00–5:30pm: Zhigang Bao (HKUST)
        Supersymmetry method and delocalization of random block band matrices

        Abstract: For large dimensional random band matrices, a famous open question is Anderson’s localization-delocalization transition for the eigenvectors, which states that the eigenvectors of the random band matrix are extended (delocalized) if the band width is larger than the square root of the matrix size, and are otherwise localized. So far, the most hopeful method to attack this question is the supersymmetry method, which is ubiquitous in physics literature. However, the rigorous justification of supersymmetry in mathematics is still notoriously difficult. In this talk, I will introduce a recent result on delocalization of random block band matrices via a rigorous supersymmetry approach. This is a joint work with László Erdös.

      Venue:  Room 210, Run Run Shaw Building, HKU   (The event is supported by the Institute of Mathematical Research, Department of Mathematics, The University of Hong Kong).