## Non-intersecting paths in the plane, loop-erased walks and random matrices.

Resumen: Non-intersecting processes in one dimension have long been an integral part of random matrix theory, at least since the pioneering work of F. Dyson in the 1960s. For planar (two-dimensional) state space processes, it is not clear how to generalize these connections since the paths under consideration are allowed to have self-intersections (or loops). In this talk, we address this problem and consider systems of random walks in planar graphs constrained to a certain type of non-intersection involving their loop-erased parts (this is closely related to connectivity probabilities of...

Read More## Discovering independent sets of maximum size in large sparse random graphs.

Resumen: Finding an independent set of maximum size is a NP-hard task on fixed graphs, and can take an exponentially long-time for optimal stochastic algorithms like Glauber dynamics with high activation rates. However, simple algorithms of polynomial complexity seem to perform well in some instances. We studied the large graph characteristics of two simple algorithms in terms of functional law of large numbers and large deviations. We are especially interested in characterizing a phase transition on the “graph landscape”, implying that some simple algorithms are asympotically...

Read More## Solución numérica de sistemas de ecuaciones diferenciales estocásticas progresivas y regresivas

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Read More## Universality of the outliers in weakly confined Coulomb gases in dimension.

Resumen: In the talk, we will study two particle systems with a strong conection to statistical physics: on one hand a class of Coulomb gases (model which describes the positions of electrons in dimension 2, attracted by a positive distribution of charges), and on the other hand zeros of random polynomials. For both models, it is known that most particules cluster in a compact set (the empirical measures converge), and we will study the existence of particles outside of this compact. We will see that these outliers converge towards a universal point process, called the Bergman point...

Read More## A new proof of Aldous-Broder theorem.

Resumen: The Aldous–Broder algorithm is a famous algorithm used to sample a uniform spanning tree of any finite connected graph G, but it is more general: it states that given a reversible M Markov chain on G started at r and up to the cover time, the tree rooted at r formed by the steps of successive first entrance in each node (different from the root) has a probability proportional to the product of these edges according to M, where the edges are directed toward r. In this talk I will present an extension to the non-reversible case and a new combinatorial proof of this theorem. Based on...

Read More## Sumas iteradas para clasificación de series de tiempo.

Resumen La clasificación de series de tiempo es una tarea recurrente en ciencia de datos. Usualmente, los datos son transformados de alguna forma para producir una representación concisa, preservando simetrías de interés. En esta charla, presentaré una serie de trabajos que describen cómo las sumas iteradas de una serie de tiempo contienen todas las cantidades (features) polinomiales invariantes bajo realinamiento temporal (time warping). Describiré también como se transforma esta representación bajo la aplicación de cierta clase funciones no lineales. Finalmente mostraré algunos ejemplos...

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