## 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 |
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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