Heat kernels for isotropic-like Markov generators on ultrametric spaces: a survey

DOI10.1134/S2070046618010016zbMath1428.46047OpenAlexW2791575629MaRDI QIDQ2317189

Alexander D. Bendikov

Publication date: 8 August 2019

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s2070046618010016

zbMATH Keywords

heat kernelultrametric spacehierarchical latticehierarchical Laplacianisotropic Markov semigroupfield of \(p\)-adic numbers \(\mathbb{Q}_{p}\)Vladimirov-Taibleson multiplier

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10)

Related Items (7)

Ultrametric diffusion, rugged energy landscapes and transition networks ⋮ Exact asymptotic formulas for the heat kernels of space and time-fractional equations ⋮ Reaction-diffusion equations on complex networks and Turing patterns, via \(p\)-adic analysis ⋮ Hierarchical Schrödinger operators with singular potentials ⋮ Poisson approximation related to spectra of hierarchical Laplacians ⋮ Ultrametric diffusion, exponential landscapes, and the first passage time problem ⋮ Non-Archimedean Coulomb gases

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