相关论文: Random Bulgarian solitaire

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…

The Bulgarian solitaire is a mathematical card game played by one person. A pack of n cards is divided into several decks (or "piles"). Each move consists of the removing of one card from each deck and collecting the removed cards to form a…

We introduce \emph{$p_n$-random $q_n$-proportion Bulgarian solitaire} ($0<p_n,q_n\le 1$), played on $n$ cards distributed in piles. In each pile, a number of cards equal to the proportion $q_n$ of the pile size rounded upward to the nearest…

Bulgarian solitaire is played on $n$ cards divided into several piles; a move consists of picking one card from each pile to form a new pile. In a recent generalization, $\sigma$-Bulgarian solitaire, the number of cards you pick from a pile…

In this article we give an exposition of Toom's proof of Bulgarian Solitaire that appeared in \emph{Kvant}. We provide more details. We also show how an application of the Chinese Remainder Theorem allows us to generalize the proof.

The Bulgarian Solitaire rule induces a finite dynamical system on the set of integer partitions of $n$. Brandt characterized and counted all cycles in its recurrent set for any given $n$, with orbits parametrized by necklaces of black and…

Bulgarian Solitaire is an interesting self-map on the set of integer partitions of a fixed number $n$. As a finite dynamical system, its long-term behavior is well-understood, having recurrent orbits parametrized by necklaces of beads with…

We study a generalized three-dimensional stadium billiard and present strong numerical evidence that this system is completely chaotic. In this convex billiard chaos is generated by the defocusing mechanism. The construction of this…

In this paper, we consider partial sums of triangular martingale differences weighted by random variables drawn uniformly on the sphere, and globally independent of the martingale differences. Starting from the so-called principle of…

We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…

Challenges for physical solitaire puzzle games are typically designed in advance by humans and limited in number. Alternatively, some games incorporate rules for stochastic setup, where the human solver randomly sets up the game board…

A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are…

Simple stochastic exchange games are based on random allocation of finite resources. These games are Markov chains that can be studied either analytically or by Monte Carlo simulations. In particular, the equilibrium distribution can be…

This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we are able to present a new rigorous result using only…

In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points:…

Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an approach to…

In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless…

We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…