p-Adic Brownian Motion as a Limit of Discrete Time Random Walks

Forfatter
Bakken, Erik Makino
Weisbart, David
Publisert
2019-05-25
Emneord
Fysikk
Kvanteteori
Permalenke
http://hdl.handle.net/123456789/94299
http://hdl.handle.net/20.500.12242/2628
DOI
10.1007/s00220-019-03447-y
Samling
Articles
Description
Bakken, Erik Makino; Weisbart, David. p-Adic Brownian Motion as a Limit of Discrete Time Random Walks. Communications in Mathematical Physics 2019 ;Volum 369.(2) s. 371-402 FF
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Sammendrag
Abstract. The p-adic di usion equation is a pseudo di erential equation that is formally analogous to the real di usion equation. The fundamental solutions to pseudo di erential equations that generalize the p-adic di usion equation give rise to p-adic Brownian motions. We show that these stochastic processes are similar to real Brownian motion in that they arise as limits of discrete time random walks on grids. While similar to those in the real case, the random walks in the p-adic setting are necessarily non-local. The study of discrete time random walks that converge to Brownian motion provides intuition about Brownian motion that is important in applications and such intuition is now available in a non-Archimedean setting.
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