Continuous Time p-Adic Random Walks and Their Path Integrals
| Autor: | Erik Makino Bakken, David Weisbart |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Pure mathematics 010308 nuclear & particles physics General Mathematics Operator (physics) Propagator Type (model theory) Random walk 01 natural sciences Hermitian matrix 0103 physical sciences Almost surely 010307 mathematical physics Continuum (set theory) Statistics Probability and Uncertainty Mathematics Probability measure |
| Zdroj: | Journal of Theoretical Probability. 32:781-805 |
| ISSN: | 1572-9230 0894-9840 |
| DOI: | 10.1007/s10959-018-0831-3 |
| Popis: | The fundamental solutions to a large class of pseudo-differential equations that generalize the formal analogy of the diffusion equation in \(\mathbb {R}\) to the groups \(p^{-n}\mathbb {Z}_p/p^{n} \mathbb {Z}_p\) give rise to probability measures on the space of Skorokhod paths on these finite groups. These measures induce probability measures on the Skorokhod space of \(\mathbb {Q}_p\)-valued paths that almost surely take values on finite grids. We study the convergence of these induced measures to their continuum limit, a p-adic Brownian motion. We additionally prove a Feynman–Kac formula for the matrix-valued propagator associated to a Schrodinger type operator acting on complex vector-valued functions on \(p^{-n}\mathbb {Z}_p/p^{n} \mathbb {Z}_p\) where the potential is a Hermitian matrix-valued multiplication operator. |
| Databáze: | OpenAIRE |
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