Number of common sites visited byNrandom walkers
نویسندگان
چکیده
منابع مشابه
Number of distinct sites visited by N random walkers.
The evaluation of the average number S N (t) of distinct sites visited up to time t by N independent random walkers all starting from the same origin on an Euclidean lattice is addressed. We find that, for the nontrivial time regime and for large N , S N (t) ≈ S N (t)(1 − ∆), where S N (t) is the volume of a hy-persphere of radius (4Dt ln N) 1/2 , ∆ =
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We calculate asymptotics for the expectation and the variance of the number of distinct sites visited by a Random Walk with Internal States. We adapt the argument of Dvoretzky and Erdős. For the two dimensional case we have to prove a local limit theorem with a remainder term, which is a generalization of the main result of [3]. AMS Subject Classification: 60J10, 82C41
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The asymptotic mean number of distinct sites visited by a subdiffusive continuous-time random walker in two dimensions seems not to have been explicitly calculated anywhere in the literature. This number has been calculated for other dimensions for only one specific asymptotic behavior of the waiting time distribution between steps. We present an explicit derivation for two cases in all integer...
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In the classical paper of Dvoretzky-Erdős [4], asymptotics for the expected value and the variance of the number of distinct sites visited by a Simple Symmetric Random Walk were calculated. Here, these results are generalized for Random Walks with Internal States. Moreover, both weak and strong laws of large numbers are proved. As a tool for these results, the error term of the local limit theo...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2012
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.86.021135