Probability Seminar of Americas
About
Probability Seminar of Americas is an (at most) twice-per-month online meeting giving researchers in probability theory and related fields an opportunity to present their results and learn about the recent progress in the field. We're experimenting with gathering afterwards in a "virtual cafe" to chat and socialize a bit after the talk. While open to everyone, the seminar is scheduled at times most convenient to those who reside in one of the time zones in the Americas. The seminar is meant to alleviate one of the problems created by the COVID19 pandemic - the cancellation of almost all in-person conferences and seminars.
Click here to request access to the Google Group email list, where we will post the zoom link.
Next Speaker: Daniel Remenik (Universidad de Chile, Santiago), 11AM PST (2PM EST)
Title: "Random Growth in 1+1 Dimensions, KPZ and KP"
Title: Random growth in 1+1 dimensions, KPZ y KP
Abstract: The KPZ fixed point is a scaling invariant Markov process which arises as the universal scaling limit of all models in the KPZ universality class, a broad collection of models including one-dimensional random growth, directed polymers and particle systems. In particular, it contains all of the rich fluctuation behavior seen in the class, which for some initial data relates to distributions from random matrix theory (RMT). In this talk I'm going to introduce this process and explain how its finite-dimensional distributions are connected to a famous integrable dispersive PDE, the Kadomtsev-Petviashvili (KP) equation (and, for some special initial data, the simpler Korteweg-de Vries equation). I will also describe how this relation provides an explanation for the appearance in the KPZ universality class of the Tracy-Widom distributions from RMT.
Board
David Aldous, UC Berkeley
Inés Armendáriz, Universidad de Buenos Aires
Krzysztof Burdzy, University of Washington
Zhen-Qing Chen, University of Washington
Christopher Hoffman, University of Washington
Russell Lyons, Indiana University
Jaime San Martín, Universidad de Chile (CMM)
Soumik Pal, University of Washington
Jason Schweinsberg, UC San Diego
Maria Eulália Vares, Universidade Federal do Rio de Janeiro
Next Speaker: Santiago Saglietti (PUC, Chile), 11AM PST (2PM EST)
Title: "Weak convergence for the scaled cover time of the rooted binary tree"
Abstract: We consider a continuous time random walk on the rooted binary tree of depth n with all transition rates equal to one and study its cover time, namely the time until all vertices of the tree have been visited. We prove that, normalized by 2^{n+1}n and then centered by (log2)n-log n, the cover time admits a weak limit as the depth of the tree tends to infinity. The limiting distribution is identified as that of a randomly shifted Gumbel random variable with rate one, where the shift is given by the unique solution to a specific distributional equation. The existence of the limit and its overall form were conjectured in the literature. However, our approach is different from those taken in earlier works on this subject and relies in great part on a comparison with the extremal landscape of the discrete Gaussian free field. Joint work with Aser Cortines and Oren Louidor.
Past Speakers
Next Speaker: February 10th: Bálint Virág, 11AM PST (2PM EST)
Title: Introduction to random plane geometry
Abstract:
If lengths 1 and 2 are assigned randomly to each edge in Z^2, what are the fluctuations of distances between far away points?
This problem is open, yet we know, in great detail, what to expect. The directed landscape, a universal random plane geometry, provides the answer to such questions.
What is the directed landscape? What does it teach us about longest increasing subsequences in random permutations, about random polymers, about models for spread of infection, about tetris, about random Schrodinger operators, and about cell biology?
Terry Lyons, February 3, 11AM PST
Title: Structure theorems for information in streamed data
Abstract: A basic question is to understand the space of real valued functions on the space of unparametrized path segments. I will explain that there are atomic ways to uniquely factor the space of “polynomial” functions on streams into two parts, a potentially expensive to compute information tensor, and a space of quick to compute polynomial functions on this informative tensor. The approach is atomic in the sense that the information in an atom from the tensor can be computed from the data without having to compute the full information. This makes the result of great potential value for situations where dimension is critical. The proofs are pure algebra. We explain that hall integrals, and hall areas are examples of uniquely informative tensors.
This work is primarily that of Cris Salvi with support from Joscha Diehl, Terry Lyons, Rosa Preiß, Jeremy Reizenstein.