Seminários de probabilidade – Segundo Semestre de 2025

Quando forem online, as palestras ocorrerão via Google Meet às segundas-feiras às 15h30, a menos de algumas exceções devidamente indicadas.

Quando forem presenciais, as palestras ocorrerão na sala C-116 às segundas-feiras às 15h30, a menos de algumas exceções devidamente indicadas.

Todas as palestras são em inglês.

Lista completa (palestras futuras podem sofrer alterações)

In this talk, we discuss how the notion of ancestry can be used to characterize the stationary distribution of the nonequilibrium Simple Exclusion Process.

Let $W$ be an $n \times n$ symmetric matrix with i.i.d. centered entries with variance one. The celebrated Wigner’s theorem states that the empirical law of eigenvalues of $W$ converges weakly to the semicircular law, which is supported on $[-2,2]$. In addition, Bai and Yin proved that the largest eigenvalue of $W$ converges to 2 almost surely. In this case, we say that there are no outliers. In this talk, we explore the universality and stability of the Bai-Yin result. If we sparsify $W$ according to a regular graph $G$, can we find conditions under which there are no outliers? This is a joint work with Dylan Altschuler, Konstantin Tikhomirov, and Pierre Youssef.

We discuss convergence results of renormalised processes and give a simplified approach to convergence of various models introduced by Toth.

De Finetti’s Theorem states that all N-indexed exchangeable sequences of real-valued random variables are mixings of i.i.d sequences. For real-valued random processes with exchangeable increments on [0, 1], Kallenberg’s 1973 result provides a complete characterisation of these processes via another mixing relationship. Continuum random trees are random tree-like metric spaces that arise naturally as scaling limits of various models of discrete random trees. In this talk, we will focus in particular on two subclasses of continuum random trees: the so-called stable trees and inhomogeneous continuum random trees. An analogue of Kallenberg’s Theorem for continuum random trees first appeared as a claim in a 2004 paper by Aldous, Miermont and Pitman. They suggested that, in much the same way that a stable bridge process on [0, 1] is a mixing of certain extremal exchangeable processes, stable trees are mixings of inhomogeneous continuum random trees.We present an outline of a rigorous argument supporting this claim, based on a novel construction that applies to both classes of trees. We will also briefly discuss some implications of this result on critical random graphs.

The talk is based on the paper Stables trees as mixings of inhomogeneous continuum random trees, Stochastic Processes and their Applications 175, 2024, 104404.

Link google meet: https://meet.google.com/idy-jhss-htx

In this work, in collaboration with Blumenthal and Taylor-Crush, I present a generalization of a fundamental result, the Gerschgorin circle theorem, to obtain enclosures of the discrete spectrum of a transfer operator preserving a strong Banach space compactly embedded in a weak Banach space.

The enclosures are obtained by rigorously bounding the weak resolvent norm of a finite rank approximation of the transfer operator.

This result has important consequences, allowing us to understand the finer statistical properties of systems satisfying a Lasota-Yorke inequality, as uniformly expanding maps and systems with additive noise by enclosing the spectrum of the associated Markov operators.