Mathematics > Probability
[Submitted on 19 Aug 2019 (v1), last revised 5 Aug 2021 (this version, v3)]
Title:Topological expansion in isomorphism theorems between matrix-valued fields and random walks
View PDFAbstract:We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fields and random walks give rise to topological expansions encoded by ribbon graphs. We further consider matrix-valued Gaussian fields twisted by an orthogonal, unitary or symplectic connection. In this case the isomorphisms involve traces of holonomies of the connection along random walk loops parametrized by boundary cycles of ribbon graphs.
Submission history
From: Titus Lupu [view email] [via CCSD proxy][v1] Mon, 19 Aug 2019 12:25:07 UTC (157 KB)
[v2] Wed, 4 Mar 2020 12:40:25 UTC (24 KB)
[v3] Thu, 5 Aug 2021 13:27:49 UTC (154 KB)
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