Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 29, 2018, 12:15 pm

Duration: 45 minutes

Location: OAT S15/S16/S17

Speaker: Johannes Obenaus

Trapping Games on Random Boards

This talk is based on a paper by R. Basu, A. E. Holroyd, J. B. Martin and J. Wästlund published in 2016.
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. In their paper, they analyze outcomes with optimal play on percolation clusters of Euclidean lattices.
They prove that, on \Z^2 with two different percolation parameters for odd and even sites, 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). It is an open question whether draws can occur when the two parameters are equal.

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