| Título: | Local Brownian property of the narrow wedge solution of the KPZ equation |
| Autores: |
Quastel, Jeremy; University of Toronto Remenik, Daniel; University of Toronto |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Kardar-Parisi-Zhang equation; stochastic heat equation; Brownian motion; finite variation; stochastic Burgers equation; random growth; asymmetric exclusion process; directed polymers 60H15; 60K35; 82C22 |
| Descripción: | Abstract. Let $H(t,x)$ be the Hopf-Cole solution at time t of the Kardar-Parisi-Zhang (KPZ) equation starting with narrow wedge initial condition, i.e. the logarithm of the solution of the multiplicative stochastic heat equation starting from a Dirac delta. Also let $H^{eq}(t,x)$ be the solution at time $t$ of the KPZ equation with the same noise, but with initial condition given by a standard two-sided Brownian motion, so that $H^{eq}(t,x)-H^{eq}(0,x)$ is itself distributed as a standard two-sided Brownian motion. We provide a simple proof of the following fact: for fixed $t$, $H(t,x)-(H^{eq}(t,x)-H^{eq}(t,0))$ is locally of finite variation. Using the same ideas we also show that if the KPZ equation is started with a two-sided Brownian motion plus a Lipschitz function then the solution stays in this class for all time. |
| Idioma: | No aplica |
1 On the Non-Convexity of the Time Constant in First-Passage Percolation por Kesten, Harry; Cornell University | 6 Simulations and Conjectures for Disconnection Exponents por Puckette, Emily E.; Occidental College,Werner, Wendelin; Université Paris-Sud and IUF |
2 A Proof of a Conjecture of Bobkov and Houdré por Kwapien, S.; Warsaw University,Pycia, M.; Warsaw University,Schachermayer, W.; University of Vienna | 7 Excursions Into a New Duality Relation for Diffusion Processes por Jansons, Kalvis M.; University College London |
3 Moderate Deviations for Martingales with Bounded Jumps por Dembo, Amir; Stanford University | 8 Percolation Beyond $Z^d$, Many Questions And a Few Answers por Benjamini, Itai; Weizmann Institute of Science,Schramm, Oded; Microsoft Research |
4 Bounds for Disconnection Exponents por Werner, Wendelin; Université Paris-Sud and IUF | 9 Transportation Approach to Some Concentration Inequalities in Product Spaces por Dembo, Amir; Stanford University,Zeitouni, Ofer; Technion - Israel Institute of Technology |
5 The Dimension of the Frontier of Planar Brownian Motion por Lawler, Gregory F.; Duke University | 10 Surface Stretching for Ornstein Uhlenbeck Velocity Fields por Carmona, Rene; Princeton University,Grishin, Stanislav; Princeton University,Xu, Lin; Princeton University,Molchanov, Stanislav; University of North Carolina at Charlotte |