### TBA by Victor-Emmanuel Brunel

- Series
- Stochastics Seminar
- Time
- Thursday, April 22, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Online TBA
- Speaker
- Victor-Emmanuel Brunel – ENSAE/CREST

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- Series
- Stochastics Seminar
- Time
- Thursday, April 22, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Online TBA
- Speaker
- Victor-Emmanuel Brunel – ENSAE/CREST

- Series
- Stochastics Seminar
- Time
- Thursday, April 15, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- David Sivakoff – The Ohio State University – dsivakoff@stat.osu.edu

At each site of Z^d, initially there is a car with probability p or a vacant parking spot with probability (1-p), and the choice is independent for all sites. Cars perform independent simple, symmetric random walks, which do not interact directly with one another, and parking spots do not move. When a car enters a site that contains a vacant spot, then the car parks at the spot and the spot is filled – both the car and the spot are removed from the system, and other cars can move freely through the site. This model exhibits a phase transition at p=1/2: all cars park almost surely if and only if p\le 1/2, and all vacant spots are filled almost surely if and only if p \ge 1/2. We study the rates of decay of cars and vacant spots at, below and above p=1/2. In many cases these rates agree with earlier findings of Bramson—Lebowitz for two-type annihilating systems wherein both particle types perform random walks at equal speeds, though we identify significantly different behavior when p<1/2. Based on joint works with Damron, Gravner, Johnson, Junge and Lyu.

Online at https://bluejeans.com/129119189

- Series
- Stochastics Seminar
- Time
- Thursday, April 8, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Galyna Livshyts – GeorgiaTech

We will discuss a conjectured sharp version of an Ehrhard-type inequality for symmetric convex sets, its connections to other questions, and partial progress towards it. We also discuss some new estimates for non-gaussian measures.

- Series
- Stochastics Seminar
- Time
- Thursday, April 1, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/129119189
- Speaker
- Anderson Y. Zhang – University of Pennsylvania

Ranking from pairwise comparisons is a central problem in a wide range of learning and social contexts. Researchers in various disciplines have made significant methodological and theoretical contributions to it. However, many fundamental statistical properties remain unclear especially for the recovery of ranking structure. This talk presents two recent projects towards optimal ranking recovery, under the Bradley-Terry-Luce (BTL) model.

In the first project, we study the problem of top-k ranking. That is, to optimally identify the set of top-k players. We derive the minimax rate and show that it can be achieved by MLE. On the other hand, we show another popular algorithm, the spectral method, is in general suboptimal.

In the second project, we study the problem of full ranking among all players. The minimax rate exhibits a transition between an exponential rate and a polynomial rate depending on the magnitude of the signal-to-noise ratio of the problem. To the best of our knowledge, this phenomenon is unique to full ranking and has not been seen in any other statistical estimation problem. A divide-and-conquer ranking algorithm is proposed to achieve the minimax rate.

- Series
- Stochastics Seminar
- Time
- Thursday, March 11, 2021 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Online TBA
- Speaker
- Matthias Löffler – ETH Zurich

- Series
- Stochastics Seminar
- Time
- Thursday, February 25, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Louis-Pierre Arguin – Baruch College, CUNY – louis-pierre.arguin@baruch.cuny.edu

I will give an account of the recent progress in probability and in number theory to understand the large values of the zeta function in small intervals of the critical line. This problem has interesting connections with the extreme value statistics of IID and log-correlated random variables.

- Series
- Stochastics Seminar
- Time
- Thursday, February 4, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Martin Wahl – Humboldt University in Berlin – martin.wahl@math.hu-berlin.de

This talk will be concerned with nonasymptotic lower bounds for the estimation of principal subspaces. I will start by reviewing some previous methods, including the local asymptotic minimax theorem and the Grassmann approach. Then I will present a new approach based on a van Trees inequality (i.e. a Bayesian version of the Cramér-Rao inequality) tailored for invariant statistical models. As applications, I will provide nonasymptotic lower bounds for principal component analysis and the matrix denoising problem, two examples that are invariant with respect to the orthogonal group. These lower bounds are characterized by doubly substochastic matrices whose entries are bounded by the different Fisher information directions, confirming recent upper bounds in the context of the empirical covariance operator.

Seminar link: https://bluejeans.com/129119189

- Series
- Stochastics Seminar
- Time
- Thursday, January 21, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
- Speaker
- Sayan Mukherjee – Duke University

Frieze showed that the expected weight of the minimum spanning tree (MST) of the uniformly weighted graph converges to ζ(3). Recently, this result was extended to a uniformly weighted simplicial complex, where the role of the MST is played by its higher-dimensional analogue -- the Minimum Spanning Acycle (MSA). In this work, we go beyond and look at the histogram of the weights in this random MSA -- both in the bulk and in the extremes. In particular, we focus on the `incomplete' setting, where one has access only to a fraction of the potential face weights. Our first result is that the empirical distribution of the MSA weights asymptotically converges to a measure based on the shadow -- the complement of graph components in higher dimensions. As far as we know, this result is the first to explore the connection between the MSA weights and the shadow. Our second result is that the extremal weights converge to an inhomogeneous Poisson point process. A interesting consequence of our two results is that we can also state the distribution of the death times in the persistence diagram corresponding to the above weighted complex, a result of interest in applied topology.

Based on joint work with Nicolas Fraiman and Gugan Thoppe, see https://arxiv.org/abs/2012.14122

- Series
- Stochastics Seminar
- Time
- Thursday, December 3, 2020 - 15:30 for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/504188361
- Speaker
- B. Cooper Boniece – Washington University in St. Louis

In the past several decades, scale invariant stochastic processes have been used in a wide range of applications including internet traffic modeling and hydrology. However, by comparison to univariate scale invariance, far less attention has been paid to characteristically multivariate models that display aspects of scaling behavior the limit theory arguably suggests is most natural.

In this talk, I will introduce a new scale invariance model called operator fractional Lévy motion and discuss some of its interesting features, as well as some aspects of wavelet-based estimation of its scaling exponents. This is related to joint work with Gustavo Didier (Tulane University), Herwig Wendt (CNRS, IRIT Univ. of Toulouse) and Patrice Abry (CNRS, ENS-Lyon).

- Series
- Stochastics Seminar
- Time
- Thursday, November 19, 2020 - 15:30 for 1 hour (actually 50 minutes)
- Location
- https://gatech.webex.com/gatech/j.php?MTID=mee147c52d7a4c0a5172f60998fee267a
- Speaker
- Tatiyana Apanasovich – George Washington University

The class which is refereed to as the Cauchy family allows for the simultaneous modeling of the long memory dependence and correlation at short and intermediate lags. We introduce a valid parametric family of cross-covariance functions for multivariate spatial random fields where each component has a covariance function from a Cauchy family. We present the conditions on the parameter space that result in valid models with varying degrees of complexity. Practical implementations, including reparameterizations to reflect the conditions on the parameter space will be discussed. We show results of various Monte Carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging. The application of the proposed multivariate Cauchy model is illustrated on a dataset from the field of Satellite Oceanography.

Link to Cisco Webex meeting: https://gatech.webex.com/gatech/j.php?MTID=mee147c52d7a4c0a5172f60998fee267a

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