Displaying similar documents to “The number of [old-time] basketball games with final score n : n where the home team was never losing but also never ahead by more than w points.”

On self-avoiding walks on certain grids and the connective constant

Dangovski, Rumen (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary: 05C81. Secondary: 60G50. We consider self-avoiding walks on the square grid graph. More precisely we investigate the number of walks of a fixed length on Z×{-1,0,1}. Using combinatorial arguments we derive the related generating function. We present the asymptotic estimates of the number of walks in consideration, as well as important connective constants.

Discrete random processes with memory: Models and applications

Tomáš Kouřim, Petr Volf (2020)

Applications of Mathematics

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The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk's future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior...

Excited random walk.

Benjamini, Itai, Wilson, David B. (2003)

Electronic Communications in Probability [electronic only]

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A note on spider walks

Christophe Gallesco, Sebastian Müller, Serguei Popov (2012)

ESAIM: Probability and Statistics

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Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.

Green functions for killed random walks in the Weyl chamber of Sp(4)

Kilian Raschel (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any ≥ 3, there is in this family a walk associated with a reflection group of order 2. Moreover, the case = 4 corresponds to a process which appears naturally by studying quantum random walks on the dual of Sp(4). For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite...