Seminarios

Karl Liechty

Título:

Propagation of critical behavior for unitary invariant plus GUE random matrices

Abstract:

It is a well known and celebrated fact that the eigenvalues of random Hermitian matrices from a unitary invariant ensemble form a determinantal point process with correlation kernel given in terms of a system of orthogonal polynomials on the real line. It is a much more recent result that the eigenvalues of the sum of such a random matrix with a matrix from the Gaussian unitary ensemble (GUE) also forms a determinantal point process, with the kernel given in terms of the Weierstrass transform of the original kernel. I’ll talk about the case in which the limiting distribution of eigenvalues is critical in the sense that there is a non-generic scaling limit for the correlation kernel, and discuss the effect of a Gaussian perturbation on the limiting critical kernel. This is joint work with Tom Claeys, Arno Kuijlaars, and Dong Wang.
nov / 2016 24

Bernardo N. B. de Lima (UFMG)

Título:

Embedding binary sequences into Bernoulli site percolation on Z3

Abstract:

We investigate the problem of embedding infinite binary sequences into Bernoulli site percolation on Zd with parameter p. In 1995, I. Benjamini and H. Kesten proved that, for d≥10 and p=1/2, all sequences can be embedded, almost surely. They conjectured that the same should hold for d≥3. We consider d≥3 and p∈(pc(d),1−pc(d)), where pc(d)<1/2 is the critical threshold for site percolation on Zd. We show that there exists an integer M=M(p), such that, a.s., every binary sequence, for which every run of consecutive {0s} or {1s} contains at least M digits, can be embedded. Joint work with M. Hilário (UFMG), P. Nolin (ETH) and V. Sidoravicius (IMPA)

nov / 2016 14

Mario Ponce (PUC)

Título:

Perfect Matchings para Grafos bipartitos aleatorios no homogéneos en medios aleatorios.

Abstract:

 Para un modelo de grafos aleatorios bipartitos en medios aleatorios, mostramos que el número de Perfect Matchings es una variable que puede ser estimada en términos de las distribuciones subyacentes de manera bastante precisa. Se trata de una aplicación de un trabajo previo acerca de permanentes de matrices dinámicamente definidas. Los resultados que veremos son parte de trabajos conjuntos con Jairo Bochi y Godofredo Iommi (UC).
nov / 2016 07

Milton Jara (IMPA)

Título:

La ecuación estocástica de Burgers

Abstract:

Introduciremos la ecuación estocástica de Burgers fraccionaria como el límite de escala de las fluctuaciones de la densidad en sistemas de partículas de largo alcance. Discutiremos su relación con la clase de universalidad KPZ y con la clase de universalidad asociada a modelos de conducción del calor en el límite de presión nula.

oct / 2016 26

Glauco Valle (UFRJ)

Título:

Exponential convergence for the Fredrikson-Andersen one spin facilitated model

Abstract:

We prove exponential convergence to equilibrium for the Fredrikson-
Andersen one spin facilitated model on bounded degree graphs under
subexponential growth condition. This was a classical conjecture related to
non-attractive spin systems. Joint work with Thomas Mountford (EPFL).

oct / 2016 17
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Departamento de Matemáticas

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Centro de Modelamiento Matemático (CMM)

Facultad de Ciencias Físicas y Matemáticas (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile