Hitting and escaping statistics: mixing, targets and holes

Henk Bruin; Mark F. Demers; Mike Todd

doi:10.1016/j.aim.2017.12.020

Hitting and escaping statistics: mixing, targets and holes

Henk Bruin, Mark F. Demers, Mike Todd

Pure Mathematics

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

Abstract

There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one can move through a natural parameter space from one to the other. On the other hand, if the mixing is subexponential, there is a phase transition between the hitting times law and the escape law.

Original language	English
Pages (from-to)	1263-1298
Number of pages	36
Journal	Advances in Mathematics
Volume	328
Early online date	22 Feb 2018
DOIs	https://doi.org/10.1016/j.aim.2017.12.020
Publication status	Published - 13 Apr 2018

Keywords

Hitting time statistics
Open systems
Escape rates
Recurrence
Mixing rates

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10.1016/j.aim.2017.12.020

hit_esc
© 2018 Elsevier Inc. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.aim.2017.12.020
Accepted author manuscript, 489 KBLicence: CC BY-NC-ND

Cite this

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abstract = "There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one can move through a natural parameter space from one to the other. On the other hand, if the mixing is subexponential, there is a phase transition between the hitting times law and the escape law.",

keywords = "Hitting time statistics, Open systems, Escape rates, Recurrence, Mixing rates",

author = "Henk Bruin and Demers, \{Mark F.\} and Mike Todd",

note = "MD was partially supported by NSF grant DMS 1362420. This project was started as part of an RIG grant through ICMS, Scotland.",

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AU - Demers, Mark F.

AU - Todd, Mike

N1 - MD was partially supported by NSF grant DMS 1362420. This project was started as part of an RIG grant through ICMS, Scotland.

PY - 2018/4/13

Y1 - 2018/4/13

N2 - There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one can move through a natural parameter space from one to the other. On the other hand, if the mixing is subexponential, there is a phase transition between the hitting times law and the escape law.

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KW - Hitting time statistics

KW - Open systems

KW - Escape rates

KW - Recurrence

KW - Mixing rates

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Hitting and escaping statistics: mixing, targets and holes

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Keywords

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Mike Todd

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Hitting and escaping statistics: mixing, targets and holes

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Mike Todd

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