SINGULAR STOCHASTIC PDEs

Convergence of the two-dimensional dynamic Ising-Kac model to $\phi₂^4$

speaker: Hendrik Weber (Warwick University)

abstract: The Kac-Ising model is spin model on a grid in which every spin interacts with a large number of neighbours. It is a popular model in statistical physics as it captures some aspects of the ``usual" Ising model, but it is often simpler to study.

We study the Glauber dynamic associated to this Kac-Ising model on a finite sub-grid of $\Z^2$ near its critical temperature. We show that in a suitable scaling the locally averaged spin field is well described by the formal stochastic PDE \[ \partial_t \Phi = \Delta \Phi - (\Phi^3 - \infty \Phi) + \xi, \] where $\xi$ denotes space time white noise, and the ``infinite constant" appears as the limit of a renormalisation procedure.

This is joint work with J.C. Mourrat.

timetable:
Tue 23 Sep, 11:30 - 12:30, Aula Dini
<< Go back