# Seminarios

## Manuel Gonzalez (Universidade de Sao Paulo)

### Título:

A ferromagnetic Ising model with periodical external field

### Abstract:

We study the low-temperature phase diagram for a two-dimensional ferromagnetic Ising model, with a periodical external magnetic field. The external field takes two values: $h$ and $-h$. The sites associated with positive and negative values of external field mimic a configuration like a chessboard with rectangular cells of sides $L_1\times L_2$ sites, such that the total value of the external field is zero.

As a main result, we apply the reflection positivity method to show the presence of a first-order phase transition. In addition, we obtain a region of uniqueness for Gibbs measure, using a uniqueness condition obtained in terms of disagreement percolation.

Joint work with Eugene Pechersky (IITP/RAS) and Anatoly Yambartsev (IME/USP)

Sala 5, Facultad de Matemáticas, Puc Chile, 17:00 hrs.

oct / 2015 06

## Inés Armendariz (Universidad de Buenos Aires)

### Título:

Metastability in a condensing zero-range process in the thermodynamic limit.

### Abstract:

Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process of the rescaled location converges to a limiting Markov process on the unit torus. This process has stationary, independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice.
Joint work with S. Grosskinsky and M. Loulakis.
ago / 2015 25

## Luiz Renato Fontes (Universidade de Sao Paulo)

### Título:

An infinite volume dynamics for the GREM with infinitely many hierarchies

### Abstract:

The K- process on a tree with k levels argueably represents an infinite volume dynamics for the GREM (Generalized Random Energy Model) with k hierarchies (under suitable conditions on its parameters). We take the limit of the former process as k diverges.

Lugar: Sala de Seminarios John Von Neumann, 7mo Piso CMM

Horario: 16:30.

jun / 2015 30

## Nathael Gozlan (U. Paris-Est Marne-La-Vallée)

### Título:

Optimal transport, concentration of measure and functional inequalities

### Abstract:

This talk is devoted to Talagrand’s transport-entropy inequalities and its deep connections to the concentration of measure phenomenon, large deviation theory and logarithmic Sobolev inequalities. After an introductive part on the field, I will present recent results obtained with P-M Samson and C. Roberto characterizing different functional inequalities in terms of concentration of measure properties.
If time enables, I will also present some works in progress about transport inequalities in a discrete setting.

Lugar: Sala de Seminarios John Von Neumann, 7mo Piso CMM

Horario: 16:30.

jun / 2015 16

## Hiep Han

### Título:

Two results concerning phase transitions: Sharp thresholds for van der Waerden's theorem and biased independent sets in regular graphs

### Abstract:

Phase transitions for random structures have been of great interest in the community of discrete mathematics in the last decades. After a brief introduction into parts of this area we shall focus on two such phenomena.

First, we will consider a sharp threshold for van der Waerden’s theorem. A subset $W$ of integers satisfies the property vdW($k$), if any two coloring of $W$ yields a monochromatic arithmetic progression of length $k$.
We consider the binomial random subset of the first $n$ integers and show that as the density increases, it exhibits a swift change from not having the property vdW($k$) to having it.

Second, we discuss the hard-core distribution for finite regular graphs. Given a graph $G$ and an activation parameter $\lambda>0$, this distribution selects a random independent set $J$ of $G$ with probability proportional to $\lambda^{|J|}$. For bipartite graphs $G$ and assuming a mild spectral condition, we show that even for rather small $\lambda$ the random independent set must be essentially contained in one of the partition classes.

The talk will be in large part introductory and non-technical. The first part is based on a joint work with E. Friedgut, M. Schacht and Y. Person and the second on a joint work with P. Tetali.

jun / 2015 10
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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)