I am co-organizing a virtual Probability Seminar with Wei-Kuo Chen and Arnab Sen at University of Minnesota for
the Spring 2023 semester. Please email me to get the Zoom link for the seminar series.
The seminar is held on Fridays at 2:30pm (ET), unless otherwise noted below.
We are also running an in-person Prob/Stat seminar series for the Spring 2023 semester.
Please find the schedule here.
02/03/2023 | Justin Ko (ENS de Lyon) |
Title: TAP Variational Principle for the Constrained Overlap Multiple Spherical Sherrington-Kirkpatrick Model. | |
Abstract: In this talk, we discuss the large deviations of overlaps from spherical spin glasses. It is known that the large deviations are given by a Parisi type variational problem. For the spherical Sherrington-Kirkpatrick model, we will show that it can also be expressed in terms of a TAP variational principle. In this setting, we are able to apply results from random matrix theory such as the asymptotics of the n-dimensional spherical integrals studied by Husson and Guionnet to derive an explicit simple form of the variational principle. The derived variational formula confirms that this model is replica symmetric for all positive temperatures, a fact which is natural but not obvious from the Parisi formula for the model. This is joint work with David Belius and Leon Frober. | |
02/10/2023 | Jinyoung Park (NYU) |
Title: Thresholds. | |
Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the "expectation-threshold") for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson-Kahn-Vu) and bounded-degree spanning trees (Montgomery). In this talk, I will present recent progress on this topic. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham. | |
02/24/2023 | Paul Simanjuntak (U Missouri) |
Title: A probabilistic approach to isoperimetric inequalities for dual L_{p} centroid bodies | |
Abstract: An isoperimetric inequality for the L_{p} centroid body for p≥1 was first proved by Lutwak, Yang, and Zhang, which extends the inequality for the dual L_{p} centroid body by Lutwak and Zhang. We show that the volume of the dual L_{p} centroid body is also maximized by the Euclidean ball for certain values of p<1, which extends Lutwak and Zhang’s result on convex bodies to star-shaped sets. This result is achieved through a probabilistic approach which associates certain random star bodies to the dual L_{p} centroid body. In this talk, we will discuss the tools used in the randomized framework and the role of certain special distribution in giving a representation of the random body. | |
03/03/2023 | Jonathan Niles-Weed (NYU) |
Title: Strong recovery of geometric planted matchings. | |
Abstract: We consider the problem of recovering a hidden matching between two correlated sets of n Gaussian samples in R^{d}. We analyze the performance of the maximum likelihood estimator, establish thresholds at which the MLE almost perfectly recovers the planted matching, and, in this regime, characterize the number of errors up to sub-polynomial factors. These results extend to the geometric setting a recent line of work on recovering matchings planted in random graphs with independently-weighted edges. Joint work with D. Kunisky (Yale). | |
03/31/2023 | Julian Sahasrabudhe (Cambridge) |
Title: An exponential improvement for diagonal Ramsey. | |
Abstract: Let R(k) be the kth diagonal Ramsey number: that is, the smallest n for which every 2-colouring of the edges of K_{n} contains a monochromatic K_{k}. In recent work with Marcelo Campos, Simon Griffiths and Rob Morris, the speaker showed that R(k) < (4-c)^{k}, for some absolute constant c>0. This is the first exponential improvement over the bound of Erdős and Szekeres, proved in 1935. In this talk I will discuss the proof. | |
04/07/2023 | Duncan Dauvergne (U Toronto) |
Title: TBA | |
Abstract: TBA | |
04/21/2023 | Nicolas Fraiman(UNC) |
Title: TBA | |
Abstract: TBA | |
04/14/2023 | Saraí Hernández-Torres (UNAM) |
Title: TBA | |
Abstract: TBA | |
04/28/2023 | Giorgio Cipolloni (Princeton) |
Title: TBA | |
Abstract: TBA | |
05/05/2023 | Reza Gheissari (Northwestern) |
Title: TBA | |
Abstract: TBA | |