Random walk on a discrete torus and random interlacements
نویسندگان
چکیده
منابع مشابه
Random Walk on a Discrete Torus and Ran- Dom Interlacements
We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ), d ≥ 3, until uN time steps, u > 0, and the model of random interlacements recently introduced by Sznitman [9]. In particular, we show that for large N , the joint distribution of the local pictures in the neighborhoods of finitely many distant points left by the walk up to t...
متن کاملOn Pinned Fields, Interlacements, and Random Walk on (z/nz)
We define two families of Poissonian soups of bidirectional trajectories on Z2, which can be seen to adequately describe the local picture of the trace left by a random walk on the two-dimensional torus (Z/NZ)2, started from the uniform distribution, run up to a time of order (N logN)2 and forced to avoid a fixed point. The local limit of the latter was recently established in [6]. Our construc...
متن کاملA Random Walk with Exponential Travel Times
Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...
متن کاملGiant Component and Vacant Set for Random Walk on a Discrete Torus
We consider random walk on a discrete torus E of side-length N , in sufficiently high dimension d. We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time uNd. We show that when u is chosen small, as N tends to infinity, there is with overwhelming probability a unique connected component in the vacan...
متن کاملRandom walks on discrete cylinders with large bases and random interlacements
Following the recent work of Sznitman [20], we investigate the microscopic picture induced by a random walk trajectory on a cylinder of the form GN ×Z, where GN is a large finite connected weighted graph, and relate it to the model of random interlacements on infinite transient weighted graphs. Under suitable assumptions, the set of points not visited by the random walk until a time of order |G...
متن کاملذخیره 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: Electronic Communications in Probability
سال: 2008
ISSN: 1083-589X
DOI: 10.1214/ecp.v13-1359