Reflection negative kernels and fractional Brownian motion
type: Item
instance of: scholarly article
title: Reflection negative kernels and fractional Brownian motion
zbMATH Open document ID: 1423.60169
published in: Symmetry
publication date: 2019-11-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1805.02593
review text: Summary: In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space \(\mathcal E\) and show in particular that fractional Brownian motion for Hurst index \(0 < H \leq 1 / 2\) is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if \(0 < H < 1 / 2\). We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of \(\mathrm{GL}_2(\mathbb{R})\). We relate this to a measure preserving action on a Gaussian \(L^2\)-Hilbert space \(L^2(\mathcal{E})\).
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 60G22
zbMATH DE Number: 7129238
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: reflection positivity
zbMATH Keywords: reflection negative kernels
zbMATH Keywords: representations of \(\mathrm{SL}_2(\mathbb{R})\)
author: Palle Jorgensen
author: Karl-Hermann Neeb
author: Gestur Ólafsson
MaRDI profile type: Publication
OpenAlex ID: W2802525818
arXiv ID: 1805.02593
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DOI: 10.3390/SYM10060191
description: scientific article