# Observatorio de I+D+i UPM

Memorias de investigación
Book chapters:
Trajectory-to-trajectory fluctuations in first passage phenomena in bounded domains
Year:2014
Research Areas
• Phisics
Information
Abstract
We study the statistics of the first passage of a random walker to absorbing subsets of the boundary of compact domains in different spatial dimensions. We describe a novel diagnostic method to quantify the trajectory-to-trajectory fluctuations of the first passage, based on the distribution of the so-called uniformity index $\omega$, measuring the similarity of the first passage times of two independent walkers starting at the same location. We show that the characteristic shape of $P(\omega)$ exhibits a transition from unimodal to bimodal, depending on the starting point of the trajectories. From the study of different geometries in one, two and three dimensions, we conclude that this transition is a generic property of first passage phenomena in bounded domains. Our results show that, in general, the Mean First Passage Time (MFPT) is a meaningful characteristic measure of the first passage behaviour only when the Brownian walkers start sufficiently far from the absorbing boundary. Strikingly, in the opposite case, the first passage statistics exhibit large trajectory-to-trajectory fluctuations and the MFPT is not representative of the actual behaviour.
International
Si
Book Edition
Book Publishing
World Scientific
ISBN
978-9814590280
Series
Book title
First-Passage Phenomena and Their Applications
From page
203
To page
225
Participants
• Autor: Thiago Mattos
• Autor: Carlos Roberto Mejia Monasterio (UPM)
• Autor: Ralf Metzler
• Autor: Gleb Oshanin
• Autor: Gregory Schehr
Research Group, Departaments and Institutes related