Zeros of the Brownian Sheet

Fuente: arXiv
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Autori principali: Chen, Keming, Woessner, Guillaume
Natura: Preprint
Pubblicazione: 2024
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author Chen, Keming
Woessner, Guillaume
author_facet Chen, Keming
Woessner, Guillaume
contents In this work we firstly answer to a question raised by Khoshnevisan in \cite[Open Problem 4]{khoshnevisan2007slices} by proving that almost surely there is no projection of big enough rank changing the Hausdorff dimension of the zeros of the Brownian sheet. Secondly, we prove that almost surely for every projection whose rank isn't matching the aforementioned condition, the projection of the zero set is the entirety of the projective space. Key words: Brownian sheet, zeros set, Hausdorff dimension, orthogonal projection.
format Preprint
id arxiv_https___arxiv_org_abs_2405_20019
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Zeros of the Brownian Sheet
Chen, Keming
Woessner, Guillaume
Probability
60G15, 60G17, 60G60
In this work we firstly answer to a question raised by Khoshnevisan in \cite[Open Problem 4]{khoshnevisan2007slices} by proving that almost surely there is no projection of big enough rank changing the Hausdorff dimension of the zeros of the Brownian sheet. Secondly, we prove that almost surely for every projection whose rank isn't matching the aforementioned condition, the projection of the zero set is the entirety of the projective space. Key words: Brownian sheet, zeros set, Hausdorff dimension, orthogonal projection.
title Zeros of the Brownian Sheet
topic Probability
60G15, 60G17, 60G60
url https://arxiv.org/abs/2405.20019