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- W1531344145 abstract "AbstractWe consider a stochastic version of Bulgarian solitaire: A numberof cards are distributed in piles; in every round a new pile is formed bycards from the old piles, and each card is picked independently witha xed probability. This game corresponds to a multi-square birth-and-death process on Young diagrams of integer partitions. We provethat this process converges in a strong sense to an exponential limitshape as the number of cards tends to in nity. Furthermore, we boundthe probability of deviation from the limit shape and relate this to thenumber of rounds played in the solitaire.Keywords: Bulgarian solitaire; birth-and-death process; limit shape;Young diagram; Markov chain 1 Introduction The game of Bulgarian solitaire is played with a deck of nidentical cardsdivided arbitrarily into several piles. A move consists of picking one cardfrom each pile and letting these cards form a new pile. This move is repeatedover and over again. If the total number of cards in the deck is a triangularnumber, i.e., n= 1 + 2 + :::+ kfor some k, this process has an interesting" @default.
- W1531344145 created "2016-06-24" @default.
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- W1531344145 date "2013-09-10" @default.
- W1531344145 modified "2023-10-03" @default.
- W1531344145 title "The Limit Shape of a Stochastic Bulgarian Solitaire" @default.
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