期刊
JOURNAL OF STATISTICAL PHYSICS
卷 166, 期 1, 页码 150-168出版社
SPRINGER
DOI: 10.1007/s10955-016-1693-7
关键词
KPZ equation; Random walk in random environment; Sharp large deviation
资金
- NSF [DMS-1208998, DMS-1613301]
- Clay Mathematics Institute through a Clay Research Fellowship
- Institute Henri Poincare through the Poincare Chair
- Packard Foundation through a Packard Fellowship for Science and Engineering
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1613301] Funding Source: National Science Foundation
We consider the transition probabilities for random walks in dimensional space-time random environments (RWRE). For critically tuned weak disorder we prove a sharp large deviation result: after appropriate rescaling, the transition probabilities for the RWRE evaluated in the large deviation regime, converge to the solution to the stochastic heat equation (SHE) with multiplicative noise (the logarithm of which is the KPZ equation). We apply this to the exactly solvable Beta RWRE and additionally present a formal derivation of the convergence of certain moment formulas for that model to those for the SHE.
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