University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Normalized functionals of first passage Brownian motion and a curious connection with the maximal relative height of fluctuating interfaces

Kearney, MJ and Martin, RJ (2016) Normalized functionals of first passage Brownian motion and a curious connection with the maximal relative height of fluctuating interfaces Journal of Physics A: Mathematical and Theoretical, 49 (19), 195001.

[img] Text
Normalized Brownian Functionals Final.pdf - Accepted version Manuscript
Restricted to Repository staff only until 12 April 2017.
Available under License : See the attached licence file.

Download (1MB)
[img]
Preview
Text (licence)
SRI_deposit_agreement.pdf
Available under License : See the attached licence file.

Download (33kB) | Preview

Abstract

A study is made of the normalized functionals {\ mathcal M} = M/T^1/2 and {\ mathcal A} = A/T^3/2 associated with one-dimensional first passage Brownian motion with positive initial condition, where M is the maximum value attained and A is the area swept out up to the random time T at which the process first reaches zero. Both {\ mathcal M} and {\ mathcal A} involve two strongly correlated random variables associated with a given Brownian path. Through their study, fresh insights are provided into the fundamental nature of such first passage processes and the underlying correlations. The probability density and the moments of {\ mathcal M} and {\ mathcal A} are calculated exactly and the theoretical results are shown to be in good agreement with those derived from simulations. Intriguingly, there is a precise equivalence in law between the variable {\ mathcal A} and the maximal relative height of the fluctuating interface in the one-dimensional Edwards-Wilkinson model with free boundary conditions. This observation leads to some interesting and still partially unresolved questions.

Item Type: Article
Subjects : Electronic Engineering; Physics
Divisions : Faculty of Engineering and Physical Sciences
Authors :
AuthorsEmailORCID
Kearney, MJUNSPECIFIEDUNSPECIFIED
Martin, RJUNSPECIFIEDUNSPECIFIED
Date : 12 April 2016
Identification Number : 10.1088/1751-8113/49/19/195001
Copyright Disclaimer : Copyright 2016 IOP Publishing
Depositing User : Symplectic Elements
Date Deposited : 08 Jul 2016 15:53
Last Modified : 08 Jul 2016 15:53
URI: http://epubs.surrey.ac.uk/id/eprint/810845

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800