131 citations · 255 across the 21 of their papers we have counts for
5 papers · 1 filter
Leading Digits of Mersenne Numbers
Zhaodong Cai, Matthew Faust, A. J. Hildebrand +2
It has long been known that sequences such as the powers of and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by…
Stationary Harmonic Measure and DLA in the Upper half Plane
Eviatar B. Procaccia, Yuan Zhang
In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion…
On sets of zero stationary harmonic measure
Eviatar B. Procaccia, Yuan Zhang
In this paper, we prove that any subset with an appropriate sub-linear horizontal growth has a non-zero stationary harmonic measure. On the other hand, we also show any subset with…
On Covering paths with 3 Dimensional Random Walk
Eviatar B. Procaccia, Yuan Zhang
In this paper we find an upper bound for the probability that a dimensional simple random walk covers each point in a nearest neighbor path connecting 0 and the boundary of an…
On Covering Monotonic Paths with Simple Random Walk
Eviatar B. Procaccia, Yuan Zhang
In this paper we study the probability that a dimensional simple random walk (or the first steps of it) covers each point in a nearest neighbor path connecting 0 and the bo…