Noticias en español
Liouville dynamical percolation & The signature method
Seminario doble conjunto Modelamiento Estocástico / Núcleo Milenio MESCYD Primera Sesión: 3pm Avelio Sepúlveda (U. Lyon 1) Liouville dynamical percolation A dynamical percolation is a process on black and white colourings of the vertices of a graph, in which each vertex has an independent Poissonian clock, and each time a clock rings the colour of its correspondent vertex is resampled. In this talk, we will study a dynamical percolation in the triangular grid, using clocks whose rate is defined in terms of a Liouville measure of parameter $\gamma$. In particular, we will show that this...
Read MoreOn Kac’s model, ideal Thermostats, and finite Reservoirs
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...
Read MoreScaling limits for a slowed random walk driven by symmetric exclusion
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.
Read MoreParticle systems and propagation of chaos for some kinetic models
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...
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