KPZ equation correlations in time
| Autor: | Alan Hammond, Promit Ghosal, Ivan Corwin |
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| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Statistical Mechanics (cond-mat.stat-mech) 010102 general mathematics Mathematical analysis Probability (math.PR) Zero (complex analysis) FOS: Physical sciences Mathematical Physics (math-ph) Space (mathematics) 01 natural sciences Wedge (geometry) 010104 statistics & probability Distribution (mathematics) Line (geometry) Exponent FOS: Mathematics 0101 mathematics Statistics Probability and Uncertainty Scaling Brownian motion Mathematics - Probability Condensed Matter - Statistical Mechanics Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1907.09317 |
| Popis: | We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic $3:2:1$ scaling of time, space and fluctuations. We study the correlation of fluctuations at two different times. We show that when the times are close to each other, the correlation approaches one at a power-law rate with exponent $2/3$, while when the two times are remote from each other, the correlation tends to zero at a power-law rate with exponent $-1/3$. We also prove exponential-type tail bounds for differences of the solution at two space-time points. Three main tools are pivotal to proving these results: 1) a representation for the two-time distribution in terms of two independent narrow wedge solutions; 2) the Brownian Gibbs property of the KPZ line ensemble; and 3) recently proved one-point tail bounds on the narrow wedge solution. Comment: 45 pages, 3 figure (this revision has two new figures and has added details in the proof of Proposition 4.3) |
| Databáze: | OpenAIRE |
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