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SUMMARY:Short paths in scale-free percolation
DTSTART;VALUE=DATE-TIME:20220804T123000Z
DTEND;VALUE=DATE-TIME:20220804T125000Z
DTSTAMP;VALUE=DATE-TIME:20240718T171821Z
UID:indico-contribution-1206@conference2.aau.at
DESCRIPTION:Graph distances in real networks\, in particular social networ
ks\, have been always in the focus of network research since Milgram's exp
eriment in 60s. In this talk we specialise in a geometric random graph kno
wn as scale-free percolation\, which shows a rich phase diagram\, and focu
s on short paths in it. In this model\, $x\,y \\in \\mathbb{Z}^d$ are conn
ected with probability depending on i.i.d weights and their Euclidean dist
ance $|x-y|$.\n\nFirst we study asymptotic distances in a regime where gra
ph distances are poly-logarithmic in Euclidean distance. With a multi-scal
e argument we obtain improved bounds on the logarithmic exponent. In the
heavy tail regime\, improvement of the upper bound shows a discrepancy wit
h the long-range percolation. In the light tail regime\, the correct expon
ent is identified.\n\nIn the following part we investigate navigation poss
ibility in the model. More precisely\, we study whether it is possible to
find the shortest paths between two vertices\, given only local informatio
n (weights and locations of neighbors). In the doubly logarithmic regime\,
a greedy routing algorithm enables us to find a comparably long path as t
he shortest one up to the prefactor.\n\nhttps://conference2.aau.at/event/1
31/contributions/1206/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1206/
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