Related papers: Heavy Hitters and Bernoulli Convolutions
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
Bernoulli random walks, a simple avalanche model, and a special branching process are essesntially identical. The identity gives alternative insights into the properties of these basic model sytems.
Annealed functional CLT in the rough path topology is proved for the standard class of ballistic random walks in random environment. Moreover, the `area anomaly', i.e. a deterministic linear correction for the second level iterated integral…
We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact…
Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. For $d \geq 2$ and $p$ strictly above the critical…
We extend the ideas of L.P. Horwitz and C. Piron and we propose a relativistic version of Event Enhanced Quantum Theory, with an event generating algorithm for spin one-half particle detectors. The algorithm is based on proper time…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
We study a large class of long-range random walks which take values on the vertices of an N dimensional hypercube. These processes are connected with multivariate Bernoulli autoregression.
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
Consider a symmetric aperiodic random walk in $Z^d$, $d\geq 3$. There are points (called heavy points) where the number of visits by the random walk is close to its maximum. We investigate the local times around these heavy points and show…
There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of…
We study a simple random walk on an n-dimensional hypercube. For any starting position we find the probability of hitting vertex a before hitting vertex b, whenever a and b share the same edge. This generalizes the model in Doyle, P., and…
The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using…
We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected graph and the trace of the simple…
The study of random walks has increasingly been popular across diverse disciplines such as statistics, mathematics, quantum physics, where they are used to model paths consisting of successive random steps in a mathematical space. A…
We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space…
We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the…