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SUMMARY:Percolation games - James Martin (Oxford)
DTSTART:20170131T163000Z
DTEND:20170131T173000Z
UID:TALK70616@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Let G be a graph (directed or undirected)\, and let v be some 
 vertex of G. Two players play the following 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 player who is unable to move loses the game. If the graph is fi
 nite\, then one player or the other must have a winning strategy. In the c
 ase of an infinite graph\, it may be that\, with optimal play\, the game c
 ontinues for ever.\n\nI'll focus in particular on games played on the latt
 ice Z^d\, directed or undirected\, with each vertex deleted independently 
 with some probability p. In the directed case\, the question of whether dr
 aws occur is closely related to ergodicity for certain probabilistic cellu
 lar automata\, and to phase transitions for the hard-core model. In the un
 directed case\, I'll describe connections to bootstrap percolation and to 
 maximum-cardinality matchings and independent sets. \n\nThis includes join
 t work with Alexander Holroyd\, Irène Marcovici\, Riddhipratim Basu\, and
  Johan Wästlund.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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