Diffusivity of a random walk on random walks
نویسندگان
چکیده
We consider a random walk ( Z (1) n , · · · , Z n ) ∈ Z with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor σ K = 2 K+2 with respect to the case of the classical simple random walk without constraint.
منابع مشابه
A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملEinstein relation for biased random walk on Galton–Watson trees
We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton–Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrary deep traps.
متن کاملLocal Limit Theorems for Random Walks in a 1D Random Environment
We consider random walks (RW) in a one-dimensional i.i.d. random environment with jumps to the nearest neighbours. For almost all environments, we prove a quenched Local Limit Theorem (LLT) for the position of the walk if the diffusivity condition is satisfied. As a corollary, we obtain the annealed version of the LLT and a new proof of the theorem of Lalley which states that the distribution o...
متن کاملDiffusivity in One - Dimensional Generalized Mott Variable - Range Hopping Models
We consider random walks in a random environment which are generalized versions of well-known effective models for Mott variable-range hopping. We study the homogenized diffusion constant of the random walk in the one-dimensional case. We prove various estimates on the low-temperature behavior which confirm and extend previous work by physicists. 1. Introduction. Random walks among randomly dis...
متن کاملFaster Clustering via Non-Backtracking Random Walks
This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-ofthe-art word2vec model to embed a graph in Euclidean space via random walks on the nodes of the graph. In VEC-NBT, we modify the original algorithm to use a non-b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 47 شماره
صفحات -
تاریخ انتشار 2015