[Probabilidad-Estadistica-Seminario] Fwd: [Todos-dm] Coloquio DM: Bálint Tóth, miércoles 18 de noviembre 11 hs

[Nicolás Frevenza]

Hola, reenvío.

Saludos

---------------
Estimadas, estimados,

tengo el placer de anunciar que el próximo coloquio del Departamento de
Matemática (FCEN-UBA) será el miércoles *18 de noviembre a las 11 horas vía
zoom*.

*Invariance Principle for the Random Lorentz Gas—Beyond the Boltzmann-Grad
Limit*
*Bálint Tóth, *University of Bristol, UK - Alfréd Rényi Institute of
Mathematics, Hungary

Understanding diffusion from first principles of physics has been a major
challenge since the groundbreaking works of Einstein, Smoluchowski, Perrin
and Langevin  in the early years of the XXth century. A simple but
mathematically (and phenomenologically, as well) sufficiently rich model is
the random Lorentz gas (proposed by H. Lorentz in 1905) where infinite-mass
spherical scatterers are placed randomly (according to a Poisson Point
Process) in R^d and point-like particles move in space observing Newton's
laws: flying free between successive specular collisions on the
infinite-mass put scatterers. Randomness comes with the initial conditions
(the positions of the put scatterers and the initial velocities of the
gas-particles) otherwise the dynamics is fully deterministic, Newtonian.
One expects that under suitable scaling the trajectory of a gas particle
looks like totally random motion (so-called "Brownian motion" of the
mathematicians). However, since the dynamics is deterministic (only the
initial conditions are random) this motion is by no means a usual random
walk - for which these type of limit theorems are well understood.

Decades ago great progress was achieved  [G. Gallavotti (1969-71), H. Spohn
(1978), C Boldrighini, L. Bunimovich, Ya Sinai (1983)] in understanding the
limiting behaviour under a particular low-density limit and finite time
horizon. In recently published  work we were able to push these results
well beyond, to time scales where the long memory of the system (due to
physical and geometric causes) is manifestly present and causes complex
difficulties.

After a survey of the historical background I will outline the mathematical
results. The main ingredients are a probabilistic coupling of the
mechanical trajectory with a Markovian random fight process, and
probabilistic and geometric controls on the efficiency of this coupling.

Based on joint work with Christopher Lutsko. Commun. Math. Phys. (2020).

Los contactaremos la semana próxima para brindarles los datos de conexión.

Pueden encontrar más información sobre el coloquio, incluyendo la lista de
futuras charlas, en
http://web.dm.uba.ar/index.php/investigacion/coloquio

Saludos cordiales,
Inés Armendáriz

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