SEMINARIO DI PROBABILITA', ANALISI STOCASTICA E STATISTICA

A weak universality result for the parabolic Anderson model

Relatore: 
Nicolas Perkowski

Abstract: We consider a class of nonlinear population models on a two-dimensional lattice which are influenced by a small random potential, and we show that on large temporal and spatial scales the population density is well described by the continuous parabolic Anderson model, a linear but singular stochastic PDE. The proof is based on a discrete formulation of paracontrolled distributions on unbounded lattices which is of independent interest because it can be applied to prove the convergence of a wide range of lattice models. This is joint work with Jörg Martin.

Data Seminario: 
Tuesday, September 26, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 10:15
Affiliazione: 
Humboldt-Universität zu Berlin
Ora Inizio: 
0000 - 09:15

Chemical reaction networks: deterministic and stochastic models

Relatore: 
Daniele Cappelletti

Chemical reaction networks are mathematical models used in
biochemistry, as well as in other fields. Specifically, the time
evolution of a system of biochemical reactions are modelled either
deterministically, by means of a system of ordinary differential
equations, or stochastically, by means of a continuous time Markov
chain. It is natural to wonder whether the dynamics of the two modelling
regimes are linked, and whether properties of one model can shed light
on the behavior of the other one. In this talk some connections will be

Data Seminario: 
Tuesday, July 4, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 12:00
Affiliazione: 
University of Wisconsin - Madison
Ora Inizio: 
0000 - 11:00

Introduction to interacting particle systems

Relatore: 
Michel Nassif

Interacting particle systems is a recently developed field in
the theory of Markov processes with many applications: particle systems
have been used to model phenomena ranging from traffic behaviour to spread
of infection and tumour growth. We introduce this field through the study
of the simple exclusion process. We will construct the generator of this
process and we will give a convergence result of the spatial particle
density to the solution of the heat equation. We will also discuss a

Data Seminario: 
Tuesday, June 27, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 13:15
Affiliazione: 
ENS Rennes
Ora Inizio: 
0000 - 12:15

Averaging along irregular curves and regularization of ODEs

Relatore: 
Remi Catellier

Paths of some stochastic processes such as fractional Brownian Motion have some amazing regularization properties. It is well known that in order to have uniqueness in differential systems such as

dy_t = b(y_t) dt,

Data Seminario: 
Tuesday, June 27, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 12:00
Affiliazione: 
Université de Nice Sophia-Antipolis
Ora Inizio: 
0000 - 11:00

Constantin and Iyer's representation formula for the Navier--Stokes equations on manifolds

Relatore: 
Dejun Luo

In this talk, we will present a probabilistic representation
formula for the Navier-Stokes equations on compact Riemannian manifolds.
Such a formula has been provided by Constantin and Iyer in the flat
case. On a Riemannian manifold, there are several different choices of
Laplacian operators acting on vector fields. We shall use the de
Rham-Hodge Laplacian operator which seems more relevant to the
probabilistic setting, and adopt Elworthy-Le Jan-Li's idea to decompose
it as a sum of the square of Lie derivatives. This is a joint work with

Data Seminario: 
Tuesday, May 16, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 12:15
Affiliazione: 
Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing
Ora Inizio: 
0000 - 11:15

Regularization by noise in (2x 2) hyperbolic systems of conservation laws

Relatore: 
C. Olivera

In this talk we study a non-strictly hyperbolic system of conservation law by stochastic perturbation. We show existence and uniqueness of the solution. We do not assume BV-regularity for the initial conditions. The proofs are based on the concept of entropy solution and on the method of charactteristics (under the influence of noise). This is the first result on the regularization by noise in hyperbolic systems of conservation law.

Data Seminario: 
Tuesday, May 23, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 12:15
Affiliazione: 
Universidade Estadual de Campinas
Ora Inizio: 
0000 - 11:15

Convergence of general weakly asymmetric exclusion processes

Relatore: 
K. Matetski

In my ongoing work with J. Quastel we consider spatially periodic growth models built from weakly asymmetric exclusion processes with finite jump ranges and general jump rates. We prove that at a large scale and after renormalization these processes converge to the Hopf-Cole solution of the KPZ equation driven by Gaussian space-time white noise. In contrast to the celebrated result by L. Bertini and G. Giacomin (in the case of the nearest neighbour interaction) and its extension by A. Dembo and L.-C.

Data Seminario: 
Tuesday, May 2, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 12:15
Affiliazione: 
University of Toronto
Ora Inizio: 
0000 - 11:15

Finite-time singularities of the stochastic harmonic map flow on surfaces

Relatore: 
A. Hocquet

Abstract: A ferromagnetic material possesses a magnetization, which, out of equilibrium, satisfies the Landau-Lifshitz-Gilbert equation (LLG). Thermal fluctuations are taken into account by Gaussian space-time white noise.

Data Seminario: 
Tuesday, July 5, 2016
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 12:30
Affiliazione: 
TU Berlin
Ora Inizio: 
0000 - 11:30

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