Positive random walks and an identity for half-space SPDEs
Shalin Parekh
Abstract
The purpose of this article is to investigate the continuum limit of a distributional identity for half-space directed polymers given in [BBC20]. The limiting identity turns out to relate the multiplicative-noise half-space stochastic heat equation with Dirichlet boundary condition to the same equation with Robin boundary condition. The identity is related to conjectured Gaussian fluctuation behavior of subcritical half-space KPZ.
Topics & Concepts
MathematicsIdentity (music)Mathematical analysisMultiplicative functionLimitingDirichlet boundary conditionSpace (punctuation)Heat equationMultiplicative noiseRandom walkLimit (mathematics)Boundary value problemStatisticsDigital signal processingEngineeringAnalog signalAcousticsSignal transfer functionPhilosophyLinguisticsElectrical engineeringPhysicsMechanical engineeringStochastic processes and statistical mechanicsRandom Matrices and Applicationsadvanced mathematical theories