Poisson asymptotics for random projections of points on a high-dimensional sphere

Itai Benjamini; Oded Schramm; Sasha Sodin

doi:https://doi.org/10.1007/s11856-011-0014-8

Poisson asymptotics for random projections of points on a high-dimensional sphere

Itai Benjamini, Oded Schramm, Sasha Sodin

Weizmann Institute of Science, Tel Aviv University

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

Abstract

Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point process.

Original language	English
Pages (from-to)	381-386
Number of pages	6
Journal	Israel Journal of Mathematics
Volume	181
Issue number	1
DOIs	https://doi.org/10.1007/s11856-011-0014-8
State	Published - Mar 2011

All Science Journal Classification (ASJC) codes

General Mathematics

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Cite this

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title = "Poisson asymptotics for random projections of points on a high-dimensional sphere",

abstract = "Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point process.",

author = "Itai Benjamini and Oded Schramm and Sasha Sodin",

note = "Israel Academy of Sciences and Humanities; ISFSupported in part by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by the ISF.",

year = "2011",

month = mar,

doi = "https://doi.org/10.1007/s11856-011-0014-8",

language = "الإنجليزيّة",

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AU - Benjamini, Itai

AU - Schramm, Oded

AU - Sodin, Sasha

N1 - Israel Academy of Sciences and Humanities; ISFSupported in part by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by the ISF.

PY - 2011/3

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N2 - Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point process.

AB - Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point process.

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U2 - https://doi.org/10.1007/s11856-011-0014-8

DO - https://doi.org/10.1007/s11856-011-0014-8

M3 - مقالة

SN - 0021-2172

VL - 181

SP - 381

EP - 386

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Poisson asymptotics for random projections of points on a high-dimensional sphere

Abstract

All Science Journal Classification (ASJC) codes

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