| Date: | August 31, 2018 |
| Time: | 11:00am |
| Location: | BLOC 628 |
| Speaker: | Alexander Roitershtein, TAMU (Statistics) |
| Title: | A random walk with catastrophes |
| Abstract: | I will discuss a discrete-time ergodic model for random population dynamics with linear growth and binomial catastrophes. In a catastrophe a large portion of the population can be eliminated with a significant probability. Through a coupling construction, we obtain sharp two-sided bounds for the rate of convergence to stationarity which are applied to show that the model exhibits a cutoff phenomenon. This is a joint work with Iddo Ben-Ari and Rinaldo B. Schinazi.
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| Date: | September 7, 2018 |
| Time: | 11:00am |
| Location: | BLOC 628 |
| Speaker: | Mir-Omid Haji-Mirsadeghi , Sharif University of Technology |
| Title: | On the notion of Dimension of Unimodular Random Graphs |
| Abstract: | In this talk we will define notions of dimension on unimodular random
graphs. The key point in this definition is unimodularity which is used
indispensably and distinguishes this view point from the previous notions which are defined in the literature. Other notions which are related to
the notion of dimension such as volume growth are discussed which provide
a toolset to calculate the dimension. Several examples of such graphs will
be discussed in relation with the theory of point processes and that of
unimodular graphs. Different methods for
finding upper bounds and lower bounds on the dimension will also be
presented and illustrated through these examples. |
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| Date: | September 28, 2018 |
| Time: | 11:00am |
| Location: | BLOC 628 |
| Speaker: | Thomas Hack, TU Wien |
| Title: | Probabilistic centroid bodies |
| Abstract: | Going back to C. Dupin and W. Blaschke, the notion of Euclidean centroid bodies, along with their associated isoperimetric inequalities, forms a classical part of the theory of convex bodies. In this talk, we focus on an empirical description of centroid bodies, that also translates to spherical space, and discuss corresponding stochastic forms of those inequalities. This is joint work with F. Besau, P. Pivovarov, and F. Schuster. |
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| Date: | November 16, 2018 |
| Time: | 10:00am |
| Location: | BLOC 220 |
| Speaker: | Eviatar B. Procaccia, TAMU |
| Title: | Stationary harmonic measure and DLA on the upper half plane |
| Abstract: | In this talk we define a version of the harmonic measure which is stationary with respect to left-right translation of the upper planar lattice. We show that this infinite stationary harmonic measure is a proper scaling limit of the classical harmonic measure. It remains open to prove that one can use the stationary harmonic measure to construct a stationary - ergodic version of diffusion limited aggregation. |
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| Date: | November 16, 2018 |
| Time: | 11:30am |
| Location: | BLOC 220 |
| Speaker: | Gordan Zitkovic, UT Austin |
| Title: | On a class of globally solvable quadratic systems of backward stochastic differential equations and applications |
| Abstract: | Backward stochastic differential equations (BSDE) emerged as a unifying language of many seemingly separate applications of stochastic analysis. While the scalar case has been well understood for almost two decades, systems are still far out of reach, even though their applications are by no means in short supply. After a short introduction to BSDEs aimed at a generic probabilist and a survey of classical results, some recent progress on fully coupled systems with quadratic nonlinearities will be described. Several applications, including stochastic equilibria in incomplete financial markets, stochastic differential games, and martingales on Riemannian manifolds will also be discussed. Joint work with Hao Xing. |
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| Date: | November 16, 2018 |
| Time: | 1:30pm |
| Location: | BLOC 220 |
| Speaker: | Eliza O'Reilly, UT Austin |
| Title: | Couplings of determinantal point processes and their reduced Palm distributions and quantifying repulsiveness |
| Abstract: | Determinantal point processes (DPPs) are a useful class of random point configurations exhibiting repulsion between points. We will describe their appealing properties and discuss a recent result on obtaining the reduced Palm distribution of a DPP by removing at most one point from the DPP. This result will be used to discuss the nature of repulsiveness of DPPs in terms of this removed point, and specific parametric models for DPPs will be compared. Additionally, we will discuss repulsion of DPPs in high dimensions and an application to high dimensional determinantal Boolean models. This talk is based on joint works with Jesper Møller and François Baccelli. |
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| Date: | November 16, 2018 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Luiz Renato Fontes, University of Sao Paulo and NYU Shanghai |
| Title: | Contact processes with general inter-recovery times |
| Abstract: | We study the contact process in d dimensions with the usual exponential infection times, of rate lambda, but with general recovery times, rather than just the usual exponential recovery times. We seek conditions on the common distribution F of the recovery times in order to have survival (of the infection, with positive probability) for either 1) all λ>0; or 2) only for λ large enough. Regarding 1), such a condition is that F satisfies some regularity conditions evocative of, but going considerably beyond, inclusion in the basin of attraction of a stable law with index less than 1. And 2) holds if a) F has two moments (by a standard, simple argument); or (more involvedly) if b) F has a greater than 1 moment and (for technical reasons) d = 1, and also F has a decreasing hazard rate. We will introduce the model and results in detail, and explain the main ideas and steps in our proofs. Joint work with Domingos Marchetti, Tom Mountford and Maria Eulália Vares.
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| Date: | November 30, 2018 |
| Time: | 11:00am |
| Location: | BLOC 628 |
| Speaker: | Amol Aggarwal, Harvard |
| Title: | GOE Statistics for Levy Matrices |
| Abstract: | Levy Matrices were introduced by Cizeau and Bouchaud in 1994. They are real, symmetric, N by N random matrices H whose upper triangular entries are independent, identically distributed $\alpha$--stable laws. We show that if $\alpha \in (1,2)$ then almost every eigenvector of H is completely delocalized and that the local spectral statistics of H in the bulk converge to those of the Gaussian Orthogonal Ensemble (GOE) as N tends to infinity. Joint work with Patrick Lopatto, Horng-Tzer Yau. |
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