Phase transition in random distance graphs on the torus
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Phase transition in random distance graphs on the torus. / Ajazi, Fioralba; Napolitano, George M.; Turova, Tatyana.
I: Journal of Applied Probability, Bind 54, Nr. 4, 12.2017, s. 1278-1294.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 54
SP - 1278
EP - 1294
JO - Journal of Applied Probability
JF - Journal of Applied Probability
SN - 0021-9002
IS - 4
ER -
ID: 189624191