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Loop-erased random walks associated with Markov processes
A. A. Dorogovtseva, I. I. Nishchenkob a Institute of mathematics of the National Academy of Sciences of Ukraine
b National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
Abstract:
A new class of loop-erased random walks (LERW) on a finite set, defined as functionals from a Markov chain is presented. We propose a scheme in which, in contrast to the general settings of LERW, the loop-erasure is performed on a non-markovian sequence and moreover, not all loops are erased with necessity. We start with a special example of a random walk with loops, the number of which at every moment of time does not exceed a given fixed number. Further we consider loop-erased random walks, for which loops are erased at random moments of time that are hitting times for a Markov chain. The asymptotics of the normalized length of such loop-erased walks is established. We estimate also the speed of convergence of the normalized length of the loop-erased random walk on a finite group to the Rayleigh distribution.
Keywords:
loop-erased random walk, Ehrenfest model.
Citation:
A. A. Dorogovtsev, I. I. Nishchenko, “Loop-erased random walks associated with Markov processes”, Theory Stoch. Process., 25(41):2 (2020), 15–24
Linking options:
https://www.mathnet.ru/eng/thsp315 https://www.mathnet.ru/eng/thsp/v25/i2/p15
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Abstract page: | 127 | Full-text PDF : | 50 | References: | 27 |
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