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 ValueatRisk
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/superadditivity 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 socalled 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). 
 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 nontrivial 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 KardarParisiZhang (KPZ) models and their universality
Abstract: The KardarParisiZhang (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 onepoint height distribution was discovered by SasamotoSpohn and AmirCorwinQuastel 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 welldefinedness. 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 multicomponent 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)

 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 leaderfollower 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 meanfield 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).

 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)
Selfinteracting random walks and statistical physics
Abstract: We start by a review of recent questions and results on selfinteracting random walks. Then we explain how the Edgereinforced 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 Edgereinforced 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

 2:00–3:30pm: Ke Wang (HKUST)
Random perturbation of lowrank 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 DavisKahan, Wedin, and Weyl, give tight estimates for the worstcase 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 OrnsteinUhlenbeck 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).

 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 MetropolisHastingstype 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 cardshuffling 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).

 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 (X_{1}, X_{2}, ... , X_{n}) over intervals of length very short compared with n. If X_{1}, X_{2},
... are i.i.d. Gaussian variables, such results are available from the
theory of Wiener process and using the celebrated KomlósMajorTusnády
(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 (BerkesLiuWu 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)
Longterm asymptotics for (fractional) Anderson models
Abstract: In this talk, I will review our recent results on
the longterm 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 FeynmnanKac 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).

 2:00–3:30pm: Pierre Nolin (CityU)
Frozen percolation and selforganized 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
"nearcritical" 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 localizationdelocalization 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).

