Brownian motion can feel the shape of a drum

Renan Gross

doi:10.1016/j.spa.2023.104233

Brownian motion can feel the shape of a drum

Renan Gross^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the scenery reconstruction problem on the d-dimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycles applies also in continuous spaces. In particular, with the right drift, Brownian motion can be used to reconstruct any scenery. To this end, we prove an injectivity property of an infinite Vandermonde matrix.(c) 2023 Elsevier B.V. All rights reserved.

Original language	English
Article number	104233
Number of pages	19
Journal	Stochastic Processes and their Applications
Volume	167
Early online date	14 Oct 2023
DOIs	https://doi.org/10.1016/j.spa.2023.104233
Publication status	Published - Jan 2024

Bibliographical note

Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.

Funding

Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.

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10.1016/j.spa.2023.104233

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title = "Brownian motion can feel the shape of a drum",

abstract = "We study the scenery reconstruction problem on the d-dimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycles applies also in continuous spaces. In particular, with the right drift, Brownian motion can be used to reconstruct any scenery. To this end, we prove an injectivity property of an infinite Vandermonde matrix.(c) 2023 Elsevier B.V. All rights reserved.",

author = "Renan Gross",

note = "Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities. ",

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AB - We study the scenery reconstruction problem on the d-dimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycles applies also in continuous spaces. In particular, with the right drift, Brownian motion can be used to reconstruct any scenery. To this end, we prove an injectivity property of an infinite Vandermonde matrix.(c) 2023 Elsevier B.V. All rights reserved.

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DO - 10.1016/j.spa.2023.104233

M3 - Article

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VL - 167

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104233

ER -

Brownian motion can feel the shape of a drum

Abstract

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