Renormalizing the Kardar–Parisi–Zhang Equation in $$d\ge 3$$ in Weak Disorder
| Autor: | Francis Comets, Clément Cosco, Chiranjib Mukherjee |
|---|---|
| Přispěvatelé: | Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2020 |
| Předmět: |
Gaussian
FOS: Physical sciences Space (mathematics) 01 natural sciences Kardar–Parisi–Zhang equation 010104 statistics & probability symbols.namesake Mathematics - Analysis of PDEs Gaussian free field FOS: Mathematics Limit (mathematics) Statistical physics 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematical Physics Physics Probability (math.PR) 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) White noise [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Rate of convergence symbols Mathematics - Probability Smoothing Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Statistical Physics Journal of Statistical Physics, Springer Verlag, 2020, 179 (3), pp.713-728. ⟨10.1007/s10955-020-02539-7⟩ |
| ISSN: | 1572-9613 0022-4715 |
| Popis: | We study Kardar–Parisi–Zhang equation in spatial dimension 3 or larger driven by a Gaussian space–time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random limit as the smoothing parameter is turned off. We identify this limit, in the case of general initial conditions ranging from flat to droplet. We provide strong approximations of the solution which obey exactly the limit law. We prove that this limit has sub-Gaussian lower tails, implying existence of all negative (and positive) moments. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
| Nepřihlášeným uživatelům se plný text nezobrazuje | K zobrazení výsledku je třeba se přihlásit. |