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SUMMARY:Large deviations for the giant in spatial random graphs - Joost Jo
rritsma (University of Oxford)
DTSTART;VALUE=DATE-TIME:20241104T170000Z
DTEND;VALUE=DATE-TIME:20241104T180000Z
UID:https://talks.ox.ac.uk/talks/id/20ce6d91-fe4e-42d5-960c-7b407145d21e/
DESCRIPTION:In (supercritical) Bernoulli bond percolation on $\\mathbb{Z}^
d$\, the proportion of vertices in the largest cluster restricted to a vol
ume-$n$ box converges to $\\theta$: the probability that the origin lies i
n an infinite cluster. The probability that this proportion is smaller tha
n $\\theta-\\varepsilon$ decays stretched exponentially with exponent stri
ctly smaller than one. The probability that the largest cluster is much la
rger than expected decays exponentially. Thus\, the upper tail decays much
faster than the lower tail. \n\nIn this talk\, we will see that the discr
epancy between the tails is reversed in supercritical spatial random graph
models in which the degrees have heavy tails. In particular\, we will foc
us on the soft heavy-tailed Poisson-Boolean model. The lower tail decays s
tretched exponentially\, with an exponent that is determined by the strong
est of three competing effects. In contrast\, the upper tail decays now po
lynomially\, and thus decays much slower than the lower tail. We will give
intuition for the exponent of this polynomial\, which is determined by th
e generating function of the finite cluster-size distribution.\n\nJoint wo
rk with Júlia Komjáthy and Dieter Mitsche.\nSpeakers:\nJoost Jorritsma (
University of Oxford)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/20ce6d91-fe4e-42d5-960c-7b407145d21e/
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DESCRIPTION:Talk:Large deviations for the giant in spatial random graphs -
Joost Jorritsma (University of Oxford)
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