The Limit Shape of a Stochastic Bulgarian Solitaire
Probability
2015-12-14 v2 Combinatorics
Abstract
We consider a stochastic version of Bulgarian solitaire: A number of cards are distributed in piles; in every round a new pile is formed by cards from the old piles, and each card is picked independently with a fixed probability. This game corresponds to a multi-square birth-and-death process on Young diagrams of integer partitions. We prove that this process converges in a strong sense to an exponential limit shape as the number of cards tends to infinity. Furthermore, we bound the probability of deviation from the limit shape and relate this to the number of rounds played in the solitaire.
Keywords
Cite
@article{arxiv.1309.2846,
title = {The Limit Shape of a Stochastic Bulgarian Solitaire},
author = {Kimmo Eriksson and Markus Jonsson and Jonas Sjöstrand},
journal= {arXiv preprint arXiv:1309.2846},
year = {2015}
}
Comments
Splitting up Theorem 1 into Theorem 1 and Theorem 2 to clarify the average shape result. Results unchanged