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Asymptotics of the Moment Generating Function for the Range of Random Walks

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Abstract

The range of random walks means the number of distinct sites visited at least once by the random walk before time n. We are interested in the free energy function of the range of simple symmetric random walks and determine the asymptotic behavior near the origin.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, Fukuoka, 812-8581, Japan

    Yuji Hamana

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  1. Yuji Hamana
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Hamana, Y. Asymptotics of the Moment Generating Function for the Range of Random Walks. Journal of Theoretical Probability 14, 189–197 (2001). https://doi.org/10.1023/A:1007829300654

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