Noticias en español
Phase Transitions on the Long Range Ising Models in presence of an random external field
Resumen: We study the ferromagnetic one-dimensiosnal Random Field Ising Model with (RFIM) in presence of an external random field. The interaction between two spins decays as $d^{\alpha-2}$ where $d$ is the distance between two sites and $\alpha \in [0,1/2)$ is a parameter of the model. We consider an external random field on $\mathbb{Z}$ with independent but not identically distributed random variables. Specifically for each $i \in \mathbb{Z}$, the distribution of $h_i$ is $P[h_i=\pm \theta(1+|i|)^{-\nu/2}]$. This work, whose main goal is the study of the existence of a phase transition at...
Read MoreThe log-Sobolev inequality for unbounded spin systems on the lattice. & Scaling limit of subcritical contact process.
PRIMERA PARTE: Expositor: Ioannis Papageorgiou (UBA) Titulo: The log-Sobolev inequality for unbounded spin systems on the lattice. Resumen: A criterion will be presented for the log-Sobolev inequality for unbounded spin systems on the lattice with non-quadratic interactions. This is a joint work with Takis Konstantopoulos (Uppsala) and James Inglis (INRIA). Furthermore, in the case of quadratic interactions, a perturbation result for the inequality will be presented. SEGUNDA PARTE: Expositora: Aurelia Deshayes (UBA) Titulo: Scaling limit of subcritical contact process Resumen: I will talk...
Read MorePercolation in hyperbolic space: the non-uniqueness phase.
Resumen: We consider Bernoulli percolation on Cayley graphs of reflection groups in the 3-dimensional hyperbolic space H^3 corresponding to a large class of Coxeter polyhedra. In such setting, we prove the existence of a non-empty no-uniqueness percolation phase, i.e., that p_c<p_u. It means that for some values of the percolation parameter there are a.s. infinitely many infinite components in the percolation subgraph. If time permits, I will present a sketch for the case of a right angled compact polyhedron with at least 18 faces.
Read MoreTerrorists never congregate in even numbers (or: some strange results in fragmentation-coalescence)
Abstract: We analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while fragmentation breaks up a cluster into a collection of singletons. Under mild conditions on the coalescence rates, we show that the distribution of cluster sizes becomes non-random in the large-scale limit. Moreover, we discover that, in the limit of small fragmentation rate, these processes exhibit a universal heavy tailed distribution with exponent 3/2. In...
Read MoreSome percolation processes with infinite-range dependencies and with inhomogeneous lines.
ABSTRACT: Consider the hyper-cubic lattice and remove the lines parallel to the coordinate axis independently at random. Does the set of remaining vertices undergo a sharp phase transition as the probability of removing the lines vary? How many connected components are there? In this talk we discuss these question for this model and for a continuous analogous model in which we remove cylinders from the Euclidian space in a isometry invariant way. We also discuss for Bernoulli bond percolation processes in the square lattice, how enhancing the parameter in a set of vertical lines...
Read MoreMacroscopic energy fluctuations: from normal diffusion to superdiffusion in the evanescent noise limit
RESUMEN: Over the last few years, anomalous behaviors have been observed for one-dimensional chains of oscillators. Recently, Bernardin, Gonçalves and Jara proved the following result: when the one-dimensional system is given by an unpinned harmonic chain of oscillators perturbed by an energy-momentum conserving noise, the energy fluctuation field at equilibrium evolves according to an infinite dimensional 3/4-fractional Ornstein-Uhlenbeck process. This talk will aim to understand the regime transition for the energy fluctuations. Let us consider the same harmonic Hamiltonian...
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