Statistical properties of sites visited by independent random walks

نویسندگان

چکیده

Abstract The set of visited sites and the number are two basic properties random walk trajectory. We consider independent walks on hyper-cubic lattices study ordering probabilities associated with these characteristics. first is probability that during time interval (0, t ), by a walker never exceeds another walker. second remain subset Using numerical simulations, we investigate leading asymptotic behaviors in spatial dimensions d = 1, 2, 3, 4. also evolution ties between sites. show analytically average increases as 1 ln 0.970 508 one dimension (ln ) 2 dimensions.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Distribution of the number of distinct sites visited by random walks in disordered lattices.

The distributions of the number of distinct sites S visited by random walks of n steps in the infinite cluster of two-dimensional lattices at the percolation threshold are studied. Different lattice sizes, different origins of the walks, and different realizations of the disorder are investigated by Monte Carlo simulations. The distribution of the mean values of (S„) appears to have selfaveragi...

متن کامل

Frequently visited sets for random walks

We study the occupation measure of various sets for a symmetric transient random walk in Z with finite variances. Let mn ðAÞ denote the occupation time of the set A up to time n. It is shown that supx2Zd m X n ðx þ AÞ= log n tends to a finite limit as n ! 1. The limit is expressed in terms of the largest eigenvalue of a matrix involving the Green function of X restricted to the set A. Some exam...

متن کامل

Statistical properties of sampled networks by random walks.

We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the original networks. From the numerical results, we find that most of topological properties of the sampled networks are almost the same as those of the origina...

متن کامل

Number of distinct sites visited by a subdiffusive random walker.

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...

متن کامل

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 , ∆ =

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment

سال: 2022

ISSN: ['1742-5468']

DOI: https://doi.org/10.1088/1742-5468/ac9619