Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Phase transition in random distance graphs on the torus

Ajazi, Fioralba LU ; Napolitano, George M. LU and Turova, Tatyana LU (2017) In Journal of Applied Probability 54(4). p.1278-1294
Abstract

In this paper we consider random distance graphs motivated by applications in neurobiology. These models can be viewed as examples of inhomogeneous random graphs, notably outside of the so-called rank-1 case. Treating these models in the context of the general theory of inhomogeneous graphs helps us to derive the asymptotics for the size of the largest connected component. In particular, we show that certain random distance graphs behave exactly as the classical ErdÅ's-Rényi model, not only in the supercritical phase (as already known) but in the subcritical case as well.

Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Inhomogeneous random graph, largest connected component, random distance graph
in
Journal of Applied Probability
volume
54
issue
4
pages
17 pages
publisher
Applied Probability Trust
external identifiers
  • scopus:85041365676
ISSN
0021-9002
DOI
10.1017/jpr.2017.63
language
English
LU publication?
yes
id
7ad6e59e-c309-4041-9755-1cffe9e1339f
date added to LUP
2018-02-12 14:09:41
date last changed
2022-04-25 05:38:48
@article{7ad6e59e-c309-4041-9755-1cffe9e1339f,
  abstract     = {{<p>In this paper we consider random distance graphs motivated by applications in neurobiology. These models can be viewed as examples of inhomogeneous random graphs, notably outside of the so-called rank-1 case. Treating these models in the context of the general theory of inhomogeneous graphs helps us to derive the asymptotics for the size of the largest connected component. In particular, we show that certain random distance graphs behave exactly as the classical ErdÅ's-Rényi model, not only in the supercritical phase (as already known) but in the subcritical case as well.</p>}},
  author       = {{Ajazi, Fioralba and Napolitano, George M. and Turova, Tatyana}},
  issn         = {{0021-9002}},
  keywords     = {{Inhomogeneous random graph; largest connected component; random distance graph}},
  language     = {{eng}},
  month        = {{12}},
  number       = {{4}},
  pages        = {{1278--1294}},
  publisher    = {{Applied Probability Trust}},
  series       = {{Journal of Applied Probability}},
  title        = {{Phase transition in random distance graphs on the torus}},
  url          = {{http://dx.doi.org/10.1017/jpr.2017.63}},
  doi          = {{10.1017/jpr.2017.63}},
  volume       = {{54}},
  year         = {{2017}},
}