2026-07-26T19:56:02Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12039 2024-03-06T10:49:14Z ddc:004 open_access

Polyharmonic Functions And Random Processes in Cones Chapon, François Fusy, Éric Raschel, Kilian Brownian motion in cones Heat kernel Random walks in cones Harmonic functions Polyharmonic functions Complete asymptotic expansions Functional equations We investigate polyharmonic functions associated to Brownian motions and random walks in cones. These are functions which cancel some power of the usual Laplacian in the continuous setting and of the discrete Laplacian in the discrete setting. We show that polyharmonic functions naturally appear while considering asymptotic expansions of the heat kernel in the Brownian case and in lattice walk enumeration problems. We provide a method to construct general polyharmonic functions through Laplace transforms and generating functions in the continuous and discrete cases, respectively. This is done by using a functional equation approach. Schloss Dagstuhl – Leibniz-Zentrum für Informatik François Chapon and Éric Fusy and Kilian Raschel 2020 Is Part Of LIPIcs, Volume 159, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2020.9 urn:nbn:de:0030-drops-120390 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.9 eng https://creativecommons.org/licenses/by/3.0/legalcode