## Seminários de probabilidade – Primeiro Semestre de 2024

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)**

This is a joint work with Rémy Sanchis and Daniel Ungaretti.

Slides Here.

This talk is based on ongoing work in collaboration with Alejandro Roldán (UdeA, Colombia), Alexander León (UdeA, Colombia) and Cristian Coletti (UFABC, Brazil).

Slides Here.

Slides Here.

Slides Here.

Link Youtube.

Slides Here.

the lengths of the shortest and longest paths between typical vertices, the maxima of these lengths from a given vertex, as well as the maxima between any two vertices; this covers the (temporal) diameter.

This talk is based on joint work with Nicolas Broutin and Nina Kamöcev.

Slides Here.

We show that a number of phase transitions take place as the turning gets slower (i.~e.~$p_n$ is getting smaller), leading first to the breakdown of the Central Limit Theorem and then to that of the Law of Large Numbers. It turns out that the critical regime is $p_n=text{const}/n$. Among the scaling limits, we obtain Uniform, Gaussian, Semicircle and Arcsine laws.

If time permits I will also discuss the random walk that coin turning generates. Here each step is 1 or -1 according to what the coin shows. In the unlikely case we have even more time, I will discuss the higher dimensional analogs of the walk.

This is joint work with Stas Volkov (Lund).

Slides Here.

Slides here

Slides here

At a large enough density, which is increasing in $lambda$ but always less than one,

such frogs on the torus form a metastable system. We prove that $n$ active frogs in a cramped torus will typically need an exponentially long time to collectively fall asleep

—exponentially long in $n$.

This completes the proof of existence of a non-trivial phase transition for this model designed for the study of self-organized criticality. This is a joint work with Amine Asselah and Nicolas Forien.