Scaling limit of WASEP to KPZ equation without Gärtner transform.
Date(s) : 21/10/2025 iCal
14h30 - 15h30
We prove that a rescaled and renormalised height function
of a weakly asymmetric simple exclusion process (WASEP) on a circle
converges to the Cole-Hopf solution of the KPZ equation.
This re-proves a well-known result by Bertini-Giacomin (’97),
with the only difference that they worked on the full line.
The main goal is to avoid Gärtner transform on the particle system,
which is a discrete version of the Cole-Hopf transform linearizing the KPZ equation.
Such nonlinear transforms are very special.
We use instead the framework of Hairer’s regularity structures
adapted to the discrete, by Erhard-Hairer (’14), Grazieschi-Matetski-Weber (’24),
and hope our approach is more robust.
In order to apply this theory,
the main technical challenge is the discrete renormalisation procedure
which requires a subtle analysis of regularity-preserving discrete convolution operators.
Based on a joint work with Konstantin Matetski and Hendrik Weber.
Emplacement
I2M Saint-Charles - Salle de séminaire
Catégories
