# Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados

## Seminario Conjunto Núcleo MESCD/ Modelamiento Escolástico

Event Date: Dec 04, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars, Stochastic Modeling

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## On Kac’s model, ideal Thermostats, and finite Reservoirs

Event Date: Dec 03, 2018 in CAPDE, Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract:   In 1956, Mark Kac introduced a stochastic model to derive a Boltzmann-like equation. Like the space-homogeneous Boltzmann’s  equation, Kac’s equation is ergodic with centered Gaussians as the  unique equilibrium state. In this talk, I will introduce Kac’s model, the thermostat used in [1] to guarantee exponentially fast convergence to equilibrium, and sketch the result in [2] how this infinite  thermostat can be approximated by a finite but large reservoir. References: [1]Bonetto, F., Loss, M.,Vaidyanathan, R.: J. Stat. Phys. 156(4), 647– 667 (2014) [2]Bonetto...

## Seminario Conjunto Núcleo MESCD/ Modelamiento Escolástico

Event Date: Nov 27, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars, Stochastic Modeling

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## Scaling limits for a slowed random walk driven by symmetric exclusion

Event Date: Aug 07, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract: Consider a simple symmetric exclusion process in one dimension, and a random walk on the same space. When on top of particles, the walker has a drift to the left, when on top of holes it has a drift to the right. Under weakly asymmetric scaling, we prove a law of large numbers and a functional central limit theorem for the position of this random walk. The proof uses techniques from the field of hydrodynamic limits to study the fluctuations of the number of particles of the in large boxes around the walker.

## Particle systems and propagation of chaos for some kinetic models

Event Date: Jun 11, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract: In this talk we will make a quick historical review of some equations arising in the classical kinetic theory of gases and related models. We will start with the Boltzmann equation, which describes the evolution of the distribution of positions and velocities of infinitely many small particles of a gas in 3-dimensional space, subjected to elastic binary collisions. We consider a finite $N$-particle system and introduce the important concept of propagation of chaos: the convergence, as $N\to\infty$ and for each time $t\geq 0$, of the distribution of the particles towards the...