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Basu, R., Holroyd, A., Martin, J. och Wästlund, J. (2016) *Trapping games on random boards*.

** BibTeX **

@article{

Basu2016,

author={Basu, Riddhipratim and Holroyd, Alexander E. and Martin, James B. and Wästlund, Johan},

title={Trapping games on random boards},

journal={Annals of Applied Probability},

issn={10505164},

volume={26},

issue={6},

pages={3727-3753},

abstract={We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with optimal play on percolation clusters of Euclidean lattices. On Z2 with two different percolation parameters for odd and even sites, we prove that the game has no draws provided closed sites of one parity are sufficiently rare compared with those of the other parity (thus favoring one player). We prove this also for certain d-dimensional lattices with d ? 3. It is an open question whether draws can occur when the two parameters are equal. On a finite ball of Z2, with only odd sites closed but with the external boundary consisting of even sites, we identify up to logarithmic factors a critical window for the trade-off between the size of the ball and the percolation parameter. Outside this window, one or the other player has a decisive advantage. Our analysis of the game is intimately tied to the effect of boundary conditions on maximum-cardinality matchings.},

year={2016},

keywords={Boundary conditions, Combinatorial game, Maximum independent set, Maximum matching, Percolation},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 247877

A1 Basu, Riddhipratim

A1 Holroyd, Alexander E.

A1 Martin, James B.

A1 Wästlund, Johan

T1 Trapping games on random boards

YR 2016

JF Annals of Applied Probability

SN 10505164

VO 26

IS 6

SP 3727

OP 3753

AB We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with optimal play on percolation clusters of Euclidean lattices. On Z2 with two different percolation parameters for odd and even sites, we prove that the game has no draws provided closed sites of one parity are sufficiently rare compared with those of the other parity (thus favoring one player). We prove this also for certain d-dimensional lattices with d ? 3. It is an open question whether draws can occur when the two parameters are equal. On a finite ball of Z2, with only odd sites closed but with the external boundary consisting of even sites, we identify up to logarithmic factors a critical window for the trade-off between the size of the ball and the percolation parameter. Outside this window, one or the other player has a decisive advantage. Our analysis of the game is intimately tied to the effect of boundary conditions on maximum-cardinality matchings.

LA eng

DO 10.1214/16-AAP1190

LK http://dx.doi.org/10.1214/16-AAP1190

OL 30