2013Fall

Probability Seminar at University of Cincinnati

Fall 2013

September 5, Thursday, Yizao Wang

1:30-2:30pm, French Hall 4206.

Title: Order statistics of heavy-tailed random variables and eigenvalues of Wigner matrices.

Abstract: We review some basic results on order statistics of heavy-tailed random variables in LePage, Woodroofe and Zinn (1981), and then their applications to the eigenvalues of Wigner matrices. The latter are recent results due to Soshnikov (2004) and Auffinger, Ben Arous and Péché (2009). 

September 12, Thursday, Wlodek Bryc

1:30-2:30pm French Hall 4206.

Title: Infinitesimal generators of the q-Meixner processes. 

Abstract: I will talk about a special class of (nonhomogeneous) Markov processes that one may call the q-Meixner processes. The main result is that the weak infinitesimal generator of the q-Meixner processes acts on bounded continuous functions with bounded continuous second derivative as a "singular integral" with respect to the orthogonality measure of an explicit family of polynomials.

Joint work with Jacek Wesolowski.

September 19, Thursday, Magda Peligrad

1:25-2:20pm French Hall 4206.

Title: Limiting spectral distribution for random matrices with correlated entries. 

Abstract: We present a method for studying the eigenvalue distribution for a n×n symmetric matrix with dependent entries. The technique is based on a blend of blocking procedure and Lindeberg's method. For a large class of random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical spectral distributions can be obtained by analyzing a Gaussian matrix with the same covariance structure. This method leads to a variety of interesting asymptotic results for matrices with dependent entries, including applications to linear processes as well as nonlinear Volterra-type processes entries. 

Based on joint work with Florence Merlevède and Marwa Banna

September 26, Thursday, no seminar.

October 3, Thursday, no seminar.

October 5-6, AMS Meeting at Louisville, Special Session on Weak Convergence in Probability and Statistics.

October 10, Thursday, no seminar (conflict with Faculty meeting).

October 10-12, 35th Midwest Probability Colloquium at Northwestern University.

October 16, Wednesday. Barnett Lecture, Ofer Zeitouni, U of Minnesota.

Title: The Ubiquity of Branching Random Walks

Room Swift 500, 5 - 6 pm

Abstract: The KPP equation describes the evolution of a front in self-interacting media. In probabilistic terms, it describes the behavior of the maximum of a system of (one dimensional) particles that perform Brownian motion between branchings. The seminal work of Bramson (1978, 1983) showed how probabilistic techniques can be used to obtain properties of solutions. I will introduce the model, discuss relevant probabilistic tools, and then show a few examples where, maybe unexpectedly, branching random walks make their appearance and lead to unexpected behavior. In particular, the free Gaussian field in the critical planar case will be discussed.

October 24, Thursday, Yizao Wang 

French Hall 4206, 1:25-2:20 pm

Title: An invariance principle for stationary random fields under Hannan's condition.

Abstract: We establish an invariance principle for stationary random fields in form of functionals of i.i.d. random variables. The condition on the weak dependence is a generalization of Hannan's condition. As an intermediate part, we establish an orthomartingale approximation. The main part of the talk will be devoted to an introduction to orthomartingales, a specific type of multiparameter martingales (there are other types as well).

Joint work with Dalibor Volny.

October 31, Thursday, Ju-Yi Yen.

French Hall 4206, 1:40-2:30pm

Title: Illustration of various methods for solving Skorokhod's embedding problem 

Abstract: We recall and illustrate three methods: Azéma-Yor algorithm, the excursion method, and the Azéma exponential result, each one allowing to solve Skorokhod's embedding problem.

November 7, Thursday, Ando Rarivoarimanana

French Hall 4206, 1:25-2:20pm

Title: Central Limit Theorem for the Unbalanced Urn Models 

Abstract: We present the central limit theorem for the unbalanced urn models. We use the technique of Mahmoud (2008) for balanced urn models. 

November 14, Thursday, Robbie Buckingham.

French Hall 4206, 1:30-2:20pm

Title: Semicircular and Catalan numbers.

November 21, Thursday, Tamer Oraby.

French Hall 4206, 1:30-2:20pm

Title: Seasonal Modeling of Chronic Wasting Disease

Abstract: Force of infection, in most of disease models, remains unchanged while parameters may vary seasonally. We developed and analyzed a summer and winter susceptible-infected (SI) model with a seasonal change in the modal form of the force of infection. We applied that model to chronic wasting disease (CWD) in deer. In this seminar, I am going to talk about the work done in that study. The talk will be intermitted with some connections of stochastic modeling to the deterministic model we used to model CWD. 

The talk is based on a joint work with Drs O. Vasilyeva, D. Krewski, F. Lutscher (University of Ottawa) and is published in the Journal of Theoretical Biology (2013).

November 22, Friday 2.00 PM – 3.30 PM,   Lindner 608. Arup Bose  (Indian Statistical Institute)   Estimation of large dimensional variance-covariance and auto covariance matrices.

November 28, Thursday, Thanksgiving break.

December 4, Wednesday, Yimin Xiao, Michigan State University

WCharlton 240, 3:35-4:35pm

Title: Gaussian Random Fields: Strong Local Nondeterminism and Fine Properties

Abstract: Self-Similar Gaussian random fields are useful as stochastic models in many applied areas and their sample functions are often random fractals. In this talk, we show that various properties of strong local nondeterminism can be applied to study fine properties (e.g. exact uniform modulus of continuity, Chung's LIL, exact Hausdorff measure functions, regularity of local times and intersection local times) of Gaussian random fields. Examples of such Gaussian random fields are solution to certain stochastic heat equation and fractional Brownian motion on sphere.

December 5, Thursday, Yimin Xiao, Michigan State University

WCharlton 247, 4-5pm

Title: Random Fields: An Introduction with Examples of Applications 

Abstract: Random fields are not only important in probability and statistics, but also widely applied as stochastic models in many scientific areas, including physics, engineering, operations research, geophysical science, agricultural sciences, environmental sciences, just to mention a few. These applications, in turn, have raised many interesting and often challenging questions for mathematicians and statisticians. 

In this talk, we will give an introduction on random fields and provide various examples of their applications, ranging from turbulence to brain imaging, from finance to geophysical science, and to cosmology. We will discuss statistically significant properties of random fields including self-similarity and long range dependence, which are vital for applications. We will show that mathematical tools from harmonic analysis, topology and geometry are useful for studying the rich probabilistic and statistical properties of random fields.

December 11, Wednesday, Adam Osękowski, Purdue University, University of Warsaw

WCharlton 120, 11:30am-12:30pm.

Title: Inequalities for martingales with values in $\ell_\infty^N$.

Abstract: 

We will establish a sharp $L^\infty\to L^1$ inequality for transforms of martingales taking values in $\ell_\infty^N$. This result is closely related to the eta-concavity characterization of UMD spaces, obtained by Lee in the 90's. The proof will rest on a construction of a certain special function, enjoying appropriate concavity and majorization.