The stochastic heat equation: Feynman-Kac formula and intermittence.
From MaRDI portal
Publication:1593216
DOI10.1007/BF02180136zbMath1080.60508MaRDI QIDQ1593216
Nicoletta Cancrini, Lorenzo Bertini
Publication date: 16 January 2001
Published in: Journal of Statistical Physics (Search for Journal in Brave)
Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Boundary theory for Markov processes (60J50)
Related Items
Large deviations of the KPZ equation via the stochastic Airy operator ⋮ Intermittency for the hyperbolic Anderson model with rough noise in space ⋮ An approximation result for a class of stochastic heat equations with colored noise ⋮ Intermittency for the wave and heat equations with fractional noise in time ⋮ Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise ⋮ On stochastic diffusion equations and stochastic Burgers’ equations ⋮ THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS ⋮ Chaotic characterization of one dimensional stochastic fractional heat equation ⋮ INTERMITTENCY AND MULTISCALING IN LIMIT THEOREMS ⋮ Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions ⋮ A forward-backward SDE from the 2D nonlinear stochastic heat equation ⋮ Determinantal structures in the O'Connell-Yor directed random polymer model ⋮ A macroscopic multifractal analysis of parabolic stochastic PDEs ⋮ Macroscaling Limit Theorems for Filtered Spatiotemporal Random Fields ⋮ Exact lower-tail large deviations of the KPZ equation ⋮ Spatial Scalings for Randomly Initialized Heat and Burgers Equations with Quadratic Potentials ⋮ KPZ line ensemble ⋮ High order Anderson parabolic model driven by rough noise in space ⋮ Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise ⋮ Weak intermittency of stochastic heat equation under discretizations ⋮ Some recent progress on stochastic heat equations ⋮ Commentary on “Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem” by David Aldous and Persi Diaconis ⋮ Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation ⋮ On the chaotic character of the stochastic heat equation. II ⋮ Renormalized-generalized solutions for the KPZ equation ⋮ Stationary solutions to the stochastic Burgers equation on the line ⋮ On the chaotic character of the stochastic heat equation, before the onset of intermitttency ⋮ Crossover distributions at the edge of the rarefaction fan ⋮ Dissipation in parabolic SPDEs ⋮ Lower tail of the KPZ equation ⋮ Constructing a solution of the \((2+1)\)-dimensional KPZ equation ⋮ Stochastic PDE limit of the six vertex model ⋮ Intermittency for stochastic partial differential equations driven by strongly inhomogeneous space-time white noises ⋮ Weak nonmild solutions to some SPDEs ⋮ The one-dimensional KPZ equation and its universality class ⋮ Gaussian scenario for the heat equation with quadratic potential and weakly dependent data with applications ⋮ Some algebraic structures in KPZ universality ⋮ Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions ⋮ A Pfaffian Representation for Flat ASEP ⋮ Directed random polymers via nested contour integrals ⋮ Lyapunov exponents of the SHE under general initial data ⋮ On the existence and position of the farthest peaks of a family of stochastic heat and wave equations ⋮ On the global maximum of the solution to a stochastic heat equation with compact-support initial data ⋮ Precise intermittency for the parabolic Anderson equation with an \((1+1)\)-dimensional time-space white noise ⋮ An averaged space-time discretization of the stochastic \(p\)-Laplace system ⋮ Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter \(H < 1/2\) ⋮ Continuity and strict positivity of the multi-layer extension of the stochastic heat equation ⋮ A multi-layer extension of the stochastic heat equation ⋮ Weakly asymmetric non-simple exclusion process and the Kardar-Parisi-Zhang equation ⋮ Fractional stochastic wave equation driven by a Gaussian noise rough in space ⋮ Scaling laws for the multidimensional Burgers equation with quadratic external potential ⋮ Enhanced group analysis of a semi linear generalization of a general bond-pricing equation ⋮ An asymptotic theory for randomly forced discrete nonlinear heat equations ⋮ Initial measures for the stochastic heat equation ⋮ Some recent progress in singular stochastic partial differential equations ⋮ Integrable probability: from representation theory to MacDonald processes ⋮ Macdonald processes ⋮ Intermittency and stochastic pseudo-differential equation with spatially inhomogeneous white noise ⋮ Moments and Lyapunov exponents for the parabolic Anderson model ⋮ A stochastic Burgers equation from a class of microscopic interactions ⋮ A brief and personal history of stochastic partial differential equations ⋮ Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions ⋮ Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz ⋮ Intermittency of superpositions of Ornstein-Uhlenbeck type processes ⋮ A PDE hierarchy for directed polymers in random environments ⋮ Some open problems in random matrix theory and the theory of integrable systems. II ⋮ Generalized solutions of the multidimensional stochastic Burgers equation ⋮ On the stochastic heat equation with spatially-colored random forcing ⋮ Spectral theory for the -Boson particle system ⋮ The continuum directed random polymer ⋮ Analysis of a stratified Kraichnan flow ⋮ Nonlinear stochastic time-fractional slow and fast diffusion equations on \(\mathbb{R}^d\) ⋮ Lyapunov exponents of the half-line SHE ⋮ Another look into the Wong-zakai theorem for stochastic heat equation ⋮ On weak convergence of stochastic heat equation with colored noise ⋮ Fractional moments of the stochastic heat equation ⋮ Gaussian fluctuations for the directed polymer partition function in dimension \(d\ge 3\) and in the whole \(L^2\)-region ⋮ Localization of directed polymers in continuous space ⋮ KPZ equation, its renormalization and invariant measures ⋮ Moments, intermittency and growth indices for the nonlinear fractional stochastic heat equation ⋮ Localization of the Gaussian multiplicative chaos in the Wiener space and the stochastic heat equation in strong disorder ⋮ Semi-discrete semi-linear parabolic SPDEs ⋮ The continuum directed polymer in Lévy noise ⋮ The intermediate disorder regime for Brownian directed polymers in Poisson environment ⋮ Spatial ergodicity for SPDEs via Poincaré-type inequalities ⋮ Upper-tail large deviation principle for the ASEP ⋮ Intermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1 ⋮ Edwards-Wilkinson fluctuations for the directed polymer in the full \(L^2\)-regime for dimensions \(d\ge 3\) ⋮ Exactly solving the KPZ equation ⋮ Intermittency for the stochastic heat equation with Lévy noise ⋮ KPZ equation tails for general initial data ⋮ The two-dimensional KPZ equation in the entire subcritical regime ⋮ The almost-sure asymptotic behavior of the solution to the stochastic heat equation with Lévy noise ⋮ Nonlinear fractional stochastic heat equation driven by Gaussian noise rough in space ⋮ Stochastic wave equations defined by fractal Laplacians on Cantor-like sets ⋮ Non-linear noise excitation and intermittency under high disorder ⋮ Strongly dependent Gaussian scenarios for the Burgers turbulence problem with quadratic external potential ⋮ Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups ⋮ Height fluctuations for the stationary KPZ equation ⋮ Exact formulas for random growth with half-flat initial data ⋮ Continuity of the solution to a stochastic time-fractional diffusion equations in the spatial domain with locally Lipschitz sources ⋮ Law of iterated logarithms and fractal properties of the KPZ equation ⋮ Solving a nonlinear fractional SPDE with spatially inhomogeneous white noise ⋮ Fluctuation exponents of the KPZ equation on a large torus ⋮ Delta-Bose gas from the viewpoint of the two-dimensional stochastic heat equation ⋮ The stochastic heat equation with multiplicative Lévy noise: existence, moments, and intermittency ⋮ Joint localization of directed polymers ⋮ Mesoscopic averaging of the two-dimensional KPZ equation ⋮ Central limit theorems for the \((2 + 1)\)-dimensional directed polymer in the weak disorder limit ⋮ Scaling limits of directed polymers in spatial-correlated environment ⋮ The critical 2d stochastic heat flow is not a Gaussian multiplicative chaos ⋮ Stationary measure for the open KPZ equation ⋮ Some recent progress on the stationary measure for the open KPZ equation ⋮ Nonlinear stochastic time-fractional diffusion equations on $\mathbb {R}$: Moments, Hölder regularity and intermittency ⋮ On a class of stochastic partial differential equations ⋮ Unnamed Item ⋮ Burgers' turbulence problem with linear or quadratic external potential ⋮ Strong solution of the stochastic Burgers equation ⋮ Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension ⋮ Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions ⋮ A stationary model of non-intersecting directed polymers
Cites Work
- Ideas in the theory of random media
- The stochastic Burgers equation
- Dynamic Scaling of Growing Interfaces
- On the support of solutions to the heat equation with noise
- The burgers equation with a noisy force and the stochastic heat equation
- Evolution equation with Gaussian potential
- Unnamed Item
- Unnamed Item
This page was built for publication: The stochastic heat equation: Feynman-Kac formula and intermittence.