Oleg Safronov, UNC Charlotte

Title: Jean Bourgain’s problem about a multi-dimensional random Schrödinger operator. Obtaining new results under weaker assumptions.

Mark Freidlin, University of Maryland

Title: Long-Time Influence of Small Perturbations

Abstract: Long-time influence of small deterministic and stochastic perturbations can be described as a motion on the simplex of invariant probability measures of the non-perturbed system. I will demonstrate this general approach in the case of  perturbations of a stochastic system with multiple stationary regimes. If the system has a first integral, the long–time behavior of the perturbed system, in an appropriate time scale, can be described by a motion on the Reeb graph of the first integral. This is a modified (because of the interior vertices of the Reeb graph)  averaging-principle-type result. If the non-perturbed stochastic system has just a finite number of ergodic invariant probability measures, the long-time behavior is defined by limit theorems for large deviations.

Isaac Sonin, UNC Charlotte

Title: The test and find problem

Abstract: We consider the following problem: k objects (balls) are allocated at random among n boxes (sites) according to some initial distribution π, no more than one object to a box. A Decision Maker (DM) can and will test all boxes. The test is not perfect, i.e. it can give false positive and false negative results. DM has m “tags”, 1 ≤ m ≤ n, and after testing all boxes she can place l tags, 0 ≤ l ≤ m on boxes she thinks have hidden objects. She is rewarded (paid) c_i for the correct guess and penalized by d_i for a wrong guess in box i. DM knows all the testing and cost parameters of the model and her goal is to maximize the expected reward. This problem can be easily generalized into a more general problem with three or more kinds of tags: “ball is here, ball is not here, not sure, etc”, and correspondingly with a more general cost structure. This problem can be classified as a problem from Statistical Decision Theory or a problem from Search Theory or as a problem from Mathematical Statistics, or even as a discrete version of an inverse problem if parameters are not completely known to DM. The origin of this model is related to the Locks, Bombs and Testing model that we discussed at the Probability seminar last semester, but the talk will be self contained. The model is quite elementary and can be understood by every graduate and even undergraduate student interested in Applied Probability and Statistics.

Stanislav Molchanov, UNC Charlotte

Title: Around the work of Kesten: Amenable Lie groups and infinite divisibility

Stanislav Molchanov, UNC Charlotte

Title: Random matrices and Wigner’s semicircle law

Stanislav Molchanov, UNC Charlotte

Title: Random determinants and Hadamard problem

Stanislav Molchanov, UNC Charlotte

Title: On the infinite divisibility of random geometric progressions

Zhiyi Zhang, UNC Charlotte

Title: Entropy Talk 02: Entropic Statistics.

Abstract: In this talk, I will introduce a framework of Entropic Statistics, including entropic sample space, 
entropic censorship, entropic distributions, entropic parameters, entropic moments, entropic basis,
and an entropic characteristic function, etc. Finally I will present two recently established results: 
two useful Gaussian processes that could serve as a basis for statistical inference. 

Zhiyi Zhang, UNC Charlotte

Title: Entropy Talk 00: What is Entropy?

Abstract: In this seminar, I would like to start with a discussion on a very fundamental question about entropy: what is entropy? After that, I would like to present some of my thoughts on several other questions: 
1) Why is Statistics (as we know it) not a bigger part of modern data sciences, such as Machine Learning and Artificial Intelligence? 
2) Why have my submitted papers been rejected from left to right by Statistics journals in recent years? 
3) What differences are there between the way of thinking in classical Statistics and that of entropy based Statistics?   

Several examples will be used to illustrate my arguments. Finally, I will present an entropic version of the Glivenko-Cantelli Theorem, 
as a fundamental theorem of entropy based Statistics.

Vladimir Panov, HSE University 

Title: Mellin Transform Techniques for Statistical Inference

Abstract: My talk is devoted to the application of Mellin transform techniques to various statistical problems arising in the context of mixture models.  For variance-mean mixtures, I will present a new semiparametric approach based on the properties of the superposition of Mellin and Laplace transforms.  Later, I will show an adaptation of this method to more complicated models of moving average Levy processes, which is closely related to a wide (and rather popular) class of models known as the ambit fields. Also we will present some new theoretical facts concerning the Mellin transform (e.g., the analogue of the Berry-Esseen inequality), which yield some fresh ideas for the statistical estimation in the classical model of multiplicative mixtures.