Conditioning schramm-loewner evolutions and loop erased random walks

Michel Bauer; Denis Bernard; Tom Kennedy

doi:10.1063/1.3097299

Conditioning schramm-loewner evolutions and loop erased random walks

Michel Bauer
, Denis Bernard
, Tom Kennedy

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

2 Scopus citations

Abstract

We discuss properties of dipolar Schramm-Loewner evolution (SLEκ) under conditioning. We show that κ=2, which describes continuum limits of loop erased random walks, is characterized as being the only value of κ such that dipolar SLE conditioned to stop on an interval coincides with dipolar SLE on that interval. We illustrate this property by computing a new bulk passage probability for SLE2.

Original language	English (US)
Article number	043301
Journal	Journal of Mathematical Physics
Volume	50
Issue number	4
DOIs	https://doi.org/10.1063/1.3097299
State	Published - 2009

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3097299

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title = "Conditioning schramm-loewner evolutions and loop erased random walks",

abstract = "We discuss properties of dipolar Schramm-Loewner evolution (SLEκ) under conditioning. We show that κ=2, which describes continuum limits of loop erased random walks, is characterized as being the only value of κ such that dipolar SLE conditioned to stop on an interval coincides with dipolar SLE on that interval. We illustrate this property by computing a new bulk passage probability for SLE2.",

author = "Michel Bauer and Denis Bernard and Tom Kennedy",

note = "Funding Information: This research began during a visit to the Kavli Institute for Theoretical Physics in September, 2006. The research of T.K. was supported in part by the National Science Foundation under Grant Nos. DMS-0501168 and DMS-0758649. The research of M.B. and D.B. was supported in part by ANR under Grant No. ANR-06-BLAN-0058. We thank the referee for useful comments and suggestions. ",

year = "2009",

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AU - Bauer, Michel

AU - Bernard, Denis

AU - Kennedy, Tom

N1 - Funding Information: This research began during a visit to the Kavli Institute for Theoretical Physics in September, 2006. The research of T.K. was supported in part by the National Science Foundation under Grant Nos. DMS-0501168 and DMS-0758649. The research of M.B. and D.B. was supported in part by ANR under Grant No. ANR-06-BLAN-0058. We thank the referee for useful comments and suggestions.

PY - 2009

Y1 - 2009

N2 - We discuss properties of dipolar Schramm-Loewner evolution (SLEκ) under conditioning. We show that κ=2, which describes continuum limits of loop erased random walks, is characterized as being the only value of κ such that dipolar SLE conditioned to stop on an interval coincides with dipolar SLE on that interval. We illustrate this property by computing a new bulk passage probability for SLE2.

AB - We discuss properties of dipolar Schramm-Loewner evolution (SLEκ) under conditioning. We show that κ=2, which describes continuum limits of loop erased random walks, is characterized as being the only value of κ such that dipolar SLE conditioned to stop on an interval coincides with dipolar SLE on that interval. We illustrate this property by computing a new bulk passage probability for SLE2.

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UR - https://www.scopus.com/pages/publications/65549101198#tab=citedBy

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JO - Journal of Mathematical Physics

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ER -

Conditioning schramm-loewner evolutions and loop erased random walks

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