A central limit theorem for random closed geodesics: Proof of the Chas–Li–Maskit conjecture

Ilya Gekhtman; Samuel J. Taylor; Giulio Tiozzo

doi:10.1016/j.aim.2019.106852

A central limit theorem for random closed geodesics: Proof of the Chas–Li–Maskit conjecture

Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo

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

Abstract

We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a conjecture of Chas–Li–Maskit.

Original language	English
Article number	106852
Journal	Advances in Mathematics
Volume	358
DOIs	https://doi.org/10.1016/j.aim.2019.106852
State	Published - 15 Dec 2019
Externally published	Yes

Keywords

Central limit theorem
Hyperbolic length
Surface groups
Word metric

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2019.106852

Cite this

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title = "A central limit theorem for random closed geodesics: Proof of the Chas–Li–Maskit conjecture",

abstract = "We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a conjecture of Chas–Li–Maskit.",

keywords = "Central limit theorem, Hyperbolic length, Surface groups, Word metric",

author = "Ilya Gekhtman and Taylor, \{Samuel J.\} and Giulio Tiozzo",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = dec,

day = "15",

doi = "10.1016/j.aim.2019.106852",

language = "الإنجليزيّة",

volume = "358",

journal = "Advances in Mathematics",

issn = "0001-8708",

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T1 - A central limit theorem for random closed geodesics

T2 - Proof of the Chas–Li–Maskit conjecture

AU - Gekhtman, Ilya

AU - Taylor, Samuel J.

AU - Tiozzo, Giulio

PY - 2019/12/15

Y1 - 2019/12/15

N2 - We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a conjecture of Chas–Li–Maskit.

AB - We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a conjecture of Chas–Li–Maskit.

KW - Central limit theorem

KW - Hyperbolic length

KW - Surface groups

KW - Word metric

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U2 - 10.1016/j.aim.2019.106852

DO - 10.1016/j.aim.2019.106852

M3 - مقالة

SN - 0001-8708

VL - 358

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 106852

ER -

A central limit theorem for random closed geodesics: Proof of the Chas–Li–Maskit conjecture

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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