Seminario de Probabilidades de Chile

Almost triangular Markov chains on ℕ

Event Date: Sep 21, 2022 in Seminario de Probabilidades de Chile, Seminars

Abstract:   A transition matrix U on ℕ is said to be almost upper triangular if U(i,j)≥0⇒j≥i−1, so that the increments of the corresponding Markov chains are at least −1; a transition matrix L on ℕ is said to be almost lower triangular if L(i,j)≥0⇒j≤i+1, and then, the increments of the corresponding Markov chains are at most +1. In this talk I will characterise the recurrence, positive recurrence and invariant distribution for the class of almost triangular transition matrices. These results encompass the case of birth and death processes (BDP), which are famous Markov chains being...

Read More

Scaling limit of the heavy-tailed ballistic deposition model with p-sticking.

Event Date: Aug 31, 2022 in Seminario de Probabilidades de Chile, Seminars

Abstract: Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of  and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. with a heavy (right) tail, and where each block sticks to the interface at the first point of contact with probability  (otherwise, it falls straight down until it lands on a block belonging to the interface). We study scaling limits of the resulting interface...

Read More

A random walk in Number Theory.

Event Date: Aug 17, 2022 in Seminario de Probabilidades de Chile, Seminars

Abstract:  Ver pdf 

Read More

The speed of invasion on an advancing population.

Event Date: Jun 15, 2022 in Seminario de Probabilidades de Chile, Seminars

Abstract:  We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional coupled F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. In that paper, it was noted that the speed of invasion by the mutant trait is faster faster when the resident population ist expanding in space compared to the speed when the resident population is already present everywhere. We use probabilistic methods, in particular  the Feynman-Kac...

Read More

El modelo de Kuramoto en grafos dinámicos aleatorios.

Event Date: Jun 01, 2022 in Seminario de Probabilidades de Chile, Seminars

Resumen: Ver Pdf.

Read More

Solution of the polynuclear growth model.

Event Date: May 18, 2022 in Seminario de Probabilidades de Chile, Seminars

Abstract:    The polynuclear growth model (PNG) is a model for crystal growth in one dimension. It is one of the most basic models in the KPZ universality class, and in the droplet geometry, it can be recast in terms of a Poissonized version of the longest increasing subsequence problem for a uniformly random permutation. In this talk, we will show how the multipoint distributions of the model can be expressed through solutions of a classical integrable system, the two-dimensional non-Abelian Toda lattice. In the appropriate scaling limit, these solutions become solutions of the KP equation,...

Read More