Jamming transitions and avalanches in the game of Dots-and-Boxes.
We study the game of Dots-and-Boxes from a statistical point of view. The early game can be treated as a case of random sequential adsorption, with a jamming transition that marks the beginning of the end game. We derive a set of differential equations to make predictions about the state of the lattice at the transition, and thus about the distribution of avalanches in the end game.
Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany.
Richard
R
Metzler
Andreas
A
Engel