Seminários de probabilidade – Primeiro 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)

We consider a system of binary interacting chains describing the dynamics of a group of N individuals that, at each time unit, either send some signal to the others or remain silent otherwise. The interactions among the chains are encoded by a directed Erdos-Renyi random graph with unknown edge probability 0<p<1. Moreover, the system is structured into two communities (excitatory chains versus inhibitory ones) which are coupled via a mean field interaction on the underlying Erdös-Rényi graph. These two communities are also unknown. Last year, I gave a talk at the DME Statistics Seminar discussing how one could estimate the edge probability p based only on the observation of the interacting chains over T time units. In this talk, I will address the complementary question of how to distinguish between the excitatory and inhibitory chains. I will also highlight some of the probabilistics tools we used to tackle this problem. The results presented are based on a joint work with Julien Chevallier (Grenoble).

Sprinkling is a technique used to control the decay of correlations (decoupling) through an inequality obtained by introducing small perturbations, and it plays a key role in multiscale renormalization schemes for strongly correlated systems. In this talk we will discuss some motivations related to two models on the top of Hammersley’s particle system and prove a sprinkled decoupling inequality for this particle system.

Sprinkling is a technique used to control the decay of correlations (decoupling) through an inequality obtained by introducing small perturbations, and it plays a key role in multiscale renormalization schemes for strongly correlated systems. In this talk we will discuss some motivations related to two models on the top of Hammersley’s particle system and prove a sprinkled decoupling inequality for this particle system.

Slides

Link meet: https://meet.google.com/qvq-kfma-qfa
In this talk, I will present recent results on the contact process on two specific types of scale-free, inhomogeneous random networks that evolve either through edge resampling or by resampling entire neighborhoods of vertices. Depending on the type of graph, the selected stationary dynamic, the tail exponent of the degree distribution, and the updating rate, we identify parameter regimes that result in either fast or slow extinction. In the latter case, we determine metastable exponents that exhibit first-order phase transitions. This is joint work with Emmanuel Jacob (ENS Lyon) and Peter Mörters (Universität zu Köln).
Link Youtube

We will present results on the existence and uniqueness of shift-invariant measures associated with substitutions in countably infinite alphabets. Specifically, we consider shift dynamical systems associated with irreducible substitutions that have well-established properties in the case of finite alphabets. Based on the properties of a matrix of countable integers related to the substitution, we can obtain results on the invariant measures such as the existence or not of invariant probability measures.

We introduce a model of epidemics among moving particles on any locally finite graph. At any time, each vertex is empty, occupied by a healthy particle, or occupied by an infected particle. Infected particles recover at rate 1 and transmit the infection to healthy particles at neighboring vertices at rate \lambda. In addition, particles perform an interchange process with rate v, that is, the states of adjacent vertices are swapped independently at rate v, allowing the infection to spread also through the movement of infected particles. On \mathbb{Z}^d, we start with a single infected particle at the origin and with all the other vertices independently occupied by a healthy particle with probability p or empty with probability 1-p. We define the threshold value \lambda_c(v,p) for \lambda above which the infection persists with positive probability and analyze its asymptotic behavior in two regimes: as v \to \infty for fixed p, in which we approach a mean-field behavior for the system, and as v \to 0 for fixed p, in which we approach a system close to the contact process on a static random environment.