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Select data courtesy of the U.S. National Library of Medicine.

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Mathematics

Subject:
Applied Mathematics
Publisher:
—
arXiv (Cornell University)
ISSN:
1435-9855
Scimago Journal Rank:
54

2017

Volume 2020
Issue 1706 (Jun)Issue 1702 (Feb)

2016

Volume 2020
Issue 1609 (Sep)

2015

Volume 2020
Issue 1502 (Feb)

2014

Volume 2020
Issue 1410 (Oct)

2013

Volume 2021
Issue 1306 (Jun)
Volume 2020
Issue 1303 (Mar)

2003

Volume 5
Issue 4 (Sep)Issue 3 (Jun)Issue 2 (Jun)Issue 1 (Mar)

2002

Volume 4
Issue 4 (Nov)Issue 3 (Sep)Issue 2 (Jun)Issue 1 (Mar)

2001

Volume 3
Issue 4 (Nov)Issue 3 (Aug)Issue 2 (May)Issue 1 (Feb)

2000

Volume 2
Issue 4 (Nov)Issue 3 (Aug)Issue 2 (Jun)Issue 1 (Mar)

1999

Volume 1
Issue 4 (Dec)Issue 3 (Sep)Issue 2 (Apr)Issue 1 (Jan)
journal article
Open Access Collection
Solidification of porous interfaces and disconnection

Nitzschner, Maximilian;Sznitman, Alain-Sol

2017 Mathematics

doi: 10.4171/JEMS/973

Abstract: In this article we obtain uniform estimates on the absorption of Brownian motion by porous interfaces surrounding a compact set. An important ingredient is the construction of certain resonance sets, which are hard to avoid for Brownian motion starting in the compact set. As an application of our results, we substantially strengthen the results of arXiv:1412.3960, and obtain when $d \ge 3$, large deviation upper bounds on the probability that simple random walk in $Z^d$, or random interlacements in $Z^d$, when their vacant set is in a strongly percolative regime, disconnect the discrete blow-up of a regular compact set from the boundary of the discrete blow-up of a box containing the compact set in its interior. Importantly, we make no convexity assumption on the compact set. It is plausible, although open at the moment, that the upper bounds that we derive in this work match in principal order the lower bounds of Xinyi Li and the second author (see arXiv:1310.2177) in the case of random interlacements, and of Xinyi Li (see arXiv:1412.3959) for the simple random walk.
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SIAM Journal on Applied MathematicsApplied Mathematics LettersApplied and Computational Harmonic AnalysisNumerical AlgorithmsAdvances in Applied MathematicsJournal of Applied MathematicsEuropean Journal of Applied MathematicsStudies in Applied MathematicsActa Applicandae MathematicaeIMA Journal of Applied Mathematics