Dr Nicholas Georgiou nicholas.georgiou@durham.ac.uk
Associate Professor
Deposition, diffusion, and nucleation on an interval
Georgiou, Nicholas; Wade, Andrew R.
Authors
Professor Andrew Wade andrew.wade@durham.ac.uk
Professor
Abstract
Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum version of a lattice model studied in the applied literature. We show that the associated interval-splitting process converges in the sparse deposition limit to a Markovian process (in the vein of Brennan and Durrett) governed by a splitting density with a compact Fourier series expansion but, apparently, no simple closed form. We show that the same splitting density governs the fixed deposition rate, large time asymptotics of the normalized gap distribution, so these asymptotics are independent of deposition rate. The splitting density is derived by solving an exit problem for planar Brownian motion from a right-angled triangle, extending work of Smith and Watson.
Citation
Georgiou, N., & Wade, A. R. (2022). Deposition, diffusion, and nucleation on an interval. Annals of Applied Probability, 32(6), 4849-4892. https://doi.org/10.1214/22-aap1804
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 27, 2022 |
Online Publication Date | Dec 6, 2022 |
Publication Date | 2022-12 |
Deposit Date | Aug 9, 2021 |
Publicly Available Date | Dec 16, 2022 |
Journal | Annals of Applied Probability |
Print ISSN | 1050-5164 |
Publisher | Institute of Mathematical Statistics |
Peer Reviewed | Peer Reviewed |
Volume | 32 |
Issue | 6 |
Pages | 4849-4892 |
DOI | https://doi.org/10.1214/22-aap1804 |
Files
Published Journal Article
(551 Kb)
PDF
You might also like
Iterated-logarithm laws for convex hulls of random walks with drift
(2023)
Journal Article
Passage-times for partially-homogeneous reflected random walks on the quadrant
(2023)
Journal Article
Cutpoints of non-homogeneous random walks
(2022)
Journal Article
Reflecting random walks in curvilinear wedges
(2021)
Book Chapter
Angular asymptotics for random walks
(2021)
Book Chapter
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search