On the (strict) positivity of solutions of the stochastic heat equation

DOI10.1214/14-AOP911zbMath1306.60088arXiv1206.1821OpenAlexW2963067769MaRDI QIDQ400574

Gregorio R. Moreno Flores

Publication date: 22 August 2014

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.1821

zbMATH Keywords

stochastic heat equationdirected polymersrandom environmentsKardar-Parisi-Zhang equation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Processes in random environments (60K37)

Related Items (20)

Large deviations of the KPZ equation via the stochastic Airy operator ⋮ The two-dimensional continuum random field Ising model ⋮ Exact lower-tail large deviations of the KPZ equation ⋮ Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equation ⋮ KPZ line ensemble ⋮ Lower tail of the KPZ equation ⋮ Renormalizing the Kardar-Parisi-Zhang equation in \(d\ge 3\) in weak disorder ⋮ Law of iterated logarithms and fractal properties of the KPZ equation ⋮ Free energy of directed polymers in random environment in \(1+1\)-dimension at high temperature ⋮ Directed random polymers via nested contour integrals ⋮ KPZ equation with a small noise, deep upper tail and limit shape ⋮ Comparison principle for stochastic heat equations driven by \(\alpha \)-stable white noises ⋮ Continuity and strict positivity of the multi-layer extension of the stochastic heat equation ⋮ KPZ reloaded ⋮ Fractional moments of the stochastic heat equation ⋮ Short time large deviations of the KPZ equation ⋮ Asymptotics of the density of parabolic Anderson random fields ⋮ Exactly solving the KPZ equation ⋮ KPZ equation tails for general initial data ⋮ The two-dimensional KPZ equation in the entire subcritical regime

Cites Work

• Regularity of the density for the stochastic heat equation
• On the partition function of a directed polymer in a Gaussian random environment
• The continuum directed random polymer
• The intermediate disorder regime for directed polymers in dimension \(1+1\)
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• On the support of solutions to the heat equation with noise
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