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CATEGORIES:Probability
SUMMARY:Percolation games - James Martin (Oxford)
DTSTART;TZID=Europe/London:20170131T163000
DTEND;TZID=Europe/London:20170131T173000
UID:TALK70616AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/70616
DESCRIPTION:Let G be a graph (directed or undirected)\, and le
t v be some vertex of G. Two players play the foll
owing game. A token starts at v. The players take
turns to move\, and each move of the game consists
of moving the token along an edge of the graph\,
to a vertex that has not yet been visited. A playe
r who is unable to move loses the game. If the gra
ph is finite\, then one player or the other must h
ave a winning strategy. In the case of an infinite
graph\, it may be that\, with optimal play\, the
game continues for ever.\n\nI'll focus in particul
ar on games played on the lattice Z^d\, directed o
r undirected\, with each vertex deleted independen
tly with some probability p. In the directed case\
, the question of whether draws occur is closely r
elated to ergodicity for certain probabilistic cel
lular automata\, and to phase transitions for the
hard-core model. In the undirected case\, I'll des
cribe connections to bootstrap percolation and to
maximum-cardinality matchings and independent sets
. \n\nThis includes joint work with Alexander Holr
oyd\, Irène Marcovici\, Riddhipratim Basu\, and Jo
han Wästlund.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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