Related papers: Better bounds for coalescing-branching random walk…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
Consider a collaborative dynamic of $k$ independent random walks on a finite connected graph $G$. We are interested in the size of the set of vertices visited by at least one walker and study how the number of walkers relates to the…
The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of…
The deterministic random walk is a deterministic process analogous to a random walk. While there are some results on the cover time of the rotor-router model, which is a deterministic random walk corresponding to a simple random walk,…
We show bounds on total variation and $L^{\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first…
The problem of constructing an optimal co-adapted coupling for a pair of symmetric random walks on $Z_2^d$ was considered by Connor and Jacka (2008), and the existence of a coupling which is stochastically fastest in the class of all such…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
We consider the nearest-neighbor simple random walk on $\Z^d$, $d\ge2$, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$. Apart from the requirement that the bonds with positive conductances percolate,…
In 2-neighborhood bootstrap percolation on a graph $G$, an infection spreads according to the following deterministic rule: infected vertices of $G$ remain infected forever and in consecutive rounds healthy vertices with at least two…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
We provide an analysis of the expected meeting time of two independent random walks on a regular graph. For 1-D circle and 2-D torus graphs, we show that the expected meeting time can be expressed as the sum of the inverse of non-zero…
We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…
We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any $\varepsilon>0$ there exists $C>1$ such that the trace of the simple random walk of length $(1+\varepsilon)n\ln{n}$ on the random…
Let $G$ be a directed graph with $n$ vertices and $m$ edges, embedded on a surface $S$, possibly with boundary, with first Betti number $\beta$. We consider the complexity of finding closed directed walks in $G$ that are either contractible…
A two-dimensional array of independent random signs produces coalescing random walks. The position of the walk, starting at the origin, after N steps is a highly nonlinear, noise sensitive function of the signs. A typical term of its…
Real networks are often dynamic. In response to it, analyses of algorithms on {\em dynamic networks} attract more and more attentions in network science and engineering. Random walks on dynamic graphs also have been investigated actively in…
In the context of a random walk on an undirected graph, Kemeny's constant can measure the average travel time for a random walk between two randomly chosen vertices. We are interested in graphs that behave counter-intuitively in regard to…
We propose the total staggered quantum walk model and the total tessellation cover of a graph. This model uses the concept of total tessellation cover to describe the motion of the walker who is allowed to hop both to vertices and edges of…
We initiate the study of what we refer to as random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that the labeling occurs increasingly whenever an unlabeled vertex is…
Consider a simple graph in which a random walk begins at a given vertex. It moves at each step with equal probability to any neighbor of its current vertex, and ends when it has visited every vertex. We call such a random walk a random…