Phase transition in random distance graphs on the torus

TY - JOUR

T1 - Phase transition in random distance graphs on the torus

AU - Ajazi, Fioralba

AU - Napolitano, George M.

AU - Turova, Tatyana

PY - 2017/12

Y1 - 2017/12

N2 - 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 Erdos-Rényi model, not only in the supercritical phase (as already known) but in the subcritical case as well.

AB - 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 Erdos-Rényi model, not only in the supercritical phase (as already known) but in the subcritical case as well.

KW - Inhomogeneous random graph

KW - largest connected component

KW - random distance graph

UR - http://www.scopus.com/inward/record.url?scp=85041365676&partnerID=8YFLogxK

U2 - 10.1017/jpr.2017.63

DO - 10.1017/jpr.2017.63

M3 - Journal article

AN - SCOPUS:85041365676

SN - 0021-9002

VL - 54

SP - 1278

EP - 1294

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 4

ER -