Abstract
The KPZ equation is one of the central objects of statistical physics, and in
the recent years it also received great attention from mathematics part. The
equation being ill-posed, it is non trivial to talk about its solutions, and
interesting to deduce any properties of these solutions. Using a connection to
the weakly asymmetric simple exclusion process we could prove some scaling
properties of the (Hopf-Cole) solution of the KPZ equation.
the recent years it also received great attention from mathematics part. The
equation being ill-posed, it is non trivial to talk about its solutions, and
interesting to deduce any properties of these solutions. Using a connection to
the weakly asymmetric simple exclusion process we could prove some scaling
properties of the (Hopf-Cole) solution of the KPZ equation.
| Original language | English |
|---|---|
| Article number | PII: S 0894-0347(2011)00692-9 |
| Pages (from-to) | 683-708 |
| Number of pages | 26 |
| Journal | Journal of the American Mathematical Society |
| Volume | 24 |
| Issue number | 3 |
| Early online date | 19 Jan 2011 |
| DOIs | |
| Publication status | Published - Jul 2011 |
Keywords
- Kardar-Parisi-Zhang equation
- stochastic heat equation
- stochastic Burgers equation
- random growth
- asymmetric exclusion process
- anomalous fluctuations
- directed polymers
- RANDOM ENVIRONMENT
- DIRECTED POLYMERS
- SUPERDIFFUSIVITY