A lower bound for disconnection by random interlacements
نویسندگان
چکیده
منابع مشابه
A lower bound for disconnection by random interlacements
We consider the vacant set of random interlacements on Z, d ≥ 3, in the percolative regime. Motivated by the large deviation principles recently obtained in [13], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates t...
متن کاملA lower bound for disconnection by simple random walk
We consider simple random walk on Z, d ≥ 3. Motivated by the work of A.-S. Sznitman and the author in [21] and [22], we investigate the asymptotic behaviour of the probability that a large body gets disconnected from infinity by the set of points visited by a simple random walk. We derive asymptotic lower bounds that bring into play random interlacements. Although open at the moment, some of th...
متن کاملA lower bound for the Chung-Diaconis-Graham random process
Chung, Diaconis, and Graham considered random processes of the form Xn+1 = anXn + bn (mod p) where p is odd, X0 = 0, an = 2 always, and bn are i.i.d. for n = 0, 1, 2, . . .. In this paper, we show that if P (bn = −1) = P (bn = 0) = P (bn = 1) = 1/3, then there exists a constant c > 1 such that c log2 p steps are not enough to make Xn get close to uniformly distributed on the integers mod p.
متن کاملA Tight Lower Bound on the Cover Time for Random
We prove that the expected time for a random walk to cover all n vertices of a graph is at least (1 + o(1))n lnn.
متن کاملA Lower Bound on the Disconnection Time of a Discrete Cylinder
We study the asymptotic behavior for large N of the disconnection time TN of simple random walk on the discrete cylinder (Z/NZ)d × Z. When d is sufficiently large, we are able to substantially improve the lower bounds on TN previously derived in [3], for d ≥ 2. We show here that the laws of N/TN are tight.
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 Journal of Probability
سال: 2014
ISSN: 1083-6489
DOI: 10.1214/ejp.v19-3067