ON THE COMING DOWN FROM INFINITY OF COALESCING BROWNIAN MOTIONS

Clayton Barnes; Leonid Mytnik; Zhenyao Sun

doi:10.1214/23-AOP1640

ON THE COMING DOWN FROM INFINITY OF COALESCING BROWNIAN MOTIONS

Clayton Barnes, Leonid Mytnik, Zhenyao Sun

School of Mathematics and Statistics

Technion-Israel Institute of Technology

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

Abstract

Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.

Original language	English
Pages (from-to)	67-92
Number of pages	26
Journal	Annals of Statistics
Volume	52
Issue number	1
DOIs	https://doi.org/10.1214/23-AOP1640
Publication status	Published - Jan 2024

Keywords

Coalescing Brownian motions
Minkowski dimension
SPDE
Shiga's duality
coming down from infinity
nonlinear PDE

Access to Document

10.1214/23-AOP1640

Cite this

@article{94651eca7f7846128f76b7acdecc144c,

title = "ON THE COMING DOWN FROM INFINITY OF COALESCING BROWNIAN MOTIONS",

abstract = "Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.",

keywords = "Coalescing Brownian motions, Minkowski dimension, SPDE, Shiga's duality, coming down from infinity, nonlinear PDE",

author = "Clayton Barnes and Leonid Mytnik and Zhenyao Sun",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2024.",

year = "2024",

month = jan,

doi = "10.1214/23-AOP1640",

language = "English",

volume = "52",

pages = "67--92",

journal = "Annals of Statistics",

issn = "0090-5364",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - ON THE COMING DOWN FROM INFINITY OF COALESCING BROWNIAN MOTIONS

AU - Barnes, Clayton

AU - Mytnik, Leonid

AU - Sun, Zhenyao

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2024.

PY - 2024/1

Y1 - 2024/1

N2 - Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.

AB - Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.

KW - Coalescing Brownian motions

KW - Minkowski dimension

KW - SPDE

KW - Shiga's duality

KW - coming down from infinity

KW - nonlinear PDE

UR - http://www.scopus.com/inward/record.url?scp=85186235170&partnerID=8YFLogxK

U2 - 10.1214/23-AOP1640

DO - 10.1214/23-AOP1640

M3 - Article

AN - SCOPUS:85186235170

SN - 0090-5364

VL - 52

SP - 67

EP - 92

JO - Annals of Statistics

JF - Annals of Statistics

IS - 1

ER -

ON THE COMING DOWN FROM INFINITY OF COALESCING BROWNIAN MOTIONS

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this