# Seminario de Probabilidad

En este seminario se expone trabajos recientes en teoría de probabilidades.
2011-01-24
Alexander Drewitz. Eth Zurich
Survival Probability of a Random Walk Among a Poisson System of Moving Traps
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - UC - 16:30 Hrs.
Abstract:
We review some old and new results on the survival probability of a random walk among a Poisson system of moving traps on the lattice, which can also be interpreted as the solution of a parabolic Anderson model with a random time-dependent potential. Furthermore, we give the sub-exponential rate of decay of the annealed survival probability in dimensions one and two, and stablish an exponential decay in higher dimensions. In addition, we show that the quenched survival probability always decays ponentially. A key ingredient is what is known in the physics literature as the Pascal principle, which asserts that the annealed survival bability is maximised if the random walk stays at a fixed position. If time admits, we will point out relations to recent rogress in the dynamic Boolean model due to Peres, Sinclair, Sousi and Stauffer.
This is joint work with Jürgen Gärtner, Alejandro F. Ramírez and Rongfeng Sun"
2011-01-10
Francis Comets. Universite de Paris Vii
Random walk with barycentric self-interaction
Sala 2 (víctor Ochsenius) - Facultad de Matemáticas - PUC 16:30 Hrs.
Abstract:
We study the asymptotic behaviour of a $d$-dimensional self-interacting random walk $X_n$ which is repelled or attracted by the
centre of mass of its previous trajectory. The walk´s trajectory ${X_1,ldots,X_n}$ can be viewed as a model for a random polymer chain in either poor or good solvent. Analysis of the random walk, and in particular $X_n - G_n$, leads to the study of time-inhomogeneous non-Markov processes $Z_n geq 0$ with one-step mean drifts of the form $$Exp [ Z_{n+1} - Z_n mid Z_n = x ] approx ho x^{-eta} - rac{x} {n},$$ where $eta > 0$ and $ho in R$. We give a recurrence classification and asymptotic theory for processes $Z_n$, which enables us to deduce asymptotic properties of $X_n - G_n$ for our self-interacting random walk.
Joint work with M
2010-12-28
Vladas Sidoravicius. Impa, Rio de Janeiro
Coordinate Percolation and Interlacement
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - PUC - 10:00 Hrs.
2010-01-10
Francis Comets. Universite de Paris Vii
Random walk with barycentric self-interaction
Sala 2 (víctor Ochsenius) - Facultad de Matemáticas - PUC - 16:30 hrs.
Abstract:
Abstract:
We study the asymptotic behaviour of a $d$-dimensional self-interacting random walk $X_n$ which is repelled or attracted by the centre of mass of its previous trajectory. The walk´s trajectory ${X_1,ldots,X_n}$ can be viewed as a model for a random polymer chain in either poor or good solvent. Analysis of the random walk, and in particular $X_n - G_n$, leads to the study of time-inhomogeneous non-Markov processes $Z_n geq 0$ with one-step mean drifts of the form $$Exp [ Z_{n+1} - Z_n mid Z_n = x ] approx ho x^{-eta} - rac{x}{n},$$ where $eta > 0$ and $ho in R$. We give a recurrence classification and asymptotic theory for processes $Z_n$, which enables us to deduce asymptotic properties of $X_n - G_n$ for our self-interacting random walk.
Joint w
2009-09-22
Alex Drewitz. Technische Universitat Berlin
Quenched exit estimates and ballisticity criteria for random walks in random enviroment
Sala de Seminario CMM, Septimo Piso. Universidad de Chile
Abstract:
Abstract:
The main results of this talk are twofold: First, we answer  affirmatively a strengthened version of a conjecture by Sznitman
concerning estimates of quenched exit probabilities. The second  subject concerns a certain class of ballisticity conditions
introduced also by Sznitman and denoted $(T)_gamma$. Although in  general the conditions are a priori more restrictive the larger $gamma$ is, it is known that the conditions are equivalent and imply  a ballistic behaviour of the RWRE for parameters in $(gamma_d, 1),$ where $gamma_d$ is a constant depending on the dimension and taking values in the interval $(0.366, 0.388).$ Here we show that for d>4, the conditions are in fact equivalent for all parameters $gamma in (0,1)$. Both results are based on techniques developed in a paper on slowdowns of RWRE by Noam Berger. This is joint work with Alejandro Ramírez.
2009-09-14
Mikhail Menshikov. University of Durham, United Kingdom
Random Walk in Random Environment with Asymptotically Zero Perturbation
Sala 3 (sector postgrado) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Abstract:
We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on Z^+ = (0,1,2,....), with reflection at the origion, where the random environment is subject to a vanishing perturbation from so called Sinai´s regime. In transient case we also study the speed" which has a logorithmic behavior.
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2009-09-07
Milton Jara. Universidad de Paris-Dauphine
Quenched scaling limits of trap models
Sala 3 - (Sector Postgrado) - Facultad de Matemáticas - UC -16:30 Hrs.
Abstract:
Resumen: We consider Bouchaud´s trap model in the d-dimensional torus. In dimension 1, we prove that the hydrodynamic limit of independent random walks following this dynamics is given by the parabolic problem associated to the FIN diffusion, which is the scaling limit of one particle in this model. In dimension d>1, we prove that the random walk is metastable in the sense of Beltran and Landim, with metastable limit given by the
K-process, introduced in this context by Fontes and Mathieu.
2004-09-10
Joaquin Fontbona. Universidad de Chile
Una Interpretación Probabilista de la Ecuación de Navier-Stokes en Dimensión 3 y Métodos de Vorticid
Sala 2 Víctor Ochsenius - Facultad de Matemáticas - 16:30 Hrs.
2003-05-23
Martin Loebl John Hubbuck. Charles University, Prague y Cmm, Santiago
Discrete Math in The Edwards-Anderson Ising Model
Sala 2, ERC, 15:00
2002-08-23
Vladas Sidoravicius. Impa, Rio de Janeiro
Some Problems From Discrete Probability
Sala 2, ERC
2002-08-22
Vladas Sidoravicius. Impa, Rio de Janeiro
Some Problems From Discrete Probability
Sala 2, ERC