Second-Order Term of Cover Time for Planar Simple Random Walk

On the Second-Order Random Walk Model for Irregular Locations

The second order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considerin...

Cover Time and Favourite Points for Planar Random

Explicit Bound on Cover Time and Cover Time of Random Walk on Complete Bipartite Graph

Counting Planar Random Walk Holes

We study two variants of the notion of holes formed by planar simple random walk of time duration 2n and the areas associated with them. We prove in both cases that the number of holes of area greater than A(n), where {A(n)} is an increasing sequence, is, up to a logarithmic correction term, asymptotic to n · A(n) for a range of large holes, thus confirming an observation by Mandelbrot. A conse...

An Lil for Cover times of Disks by Planar Random Walk and Wiener Sausage

Let Rn be the radius of the largest disk covered after n steps of a simple random walk. We prove that almost surely lim sup n→∞ (logRn)/(log n log3 n) = 1/4, where log3 denotes 3 iterations of the log function. This is motivated by a question of Erdős and Taylor. We also obtain the analogous result for the Wiener sausage, refining a result of Meyre and Werner.