131 citations · 255 across the 21 of their papers we have counts for
8 papers · 1 filter
Stationary Harmonic Measure as the Scaling Limit of Truncated Harmonic Measure
Eviatar B. Procaccia, Jiayan Ye, Yuan Zhang
In this paper we prove that the stationary harmonic measure of an infinite set in the upper planar lattice can be represented as the proper scaling limit of the classical harmonic…
Stabilization of DLA in a wedge
Eviatar B. Procaccia, Ron Rosenthal, Yuan Zhang
We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than , there is some such that almost sure…
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…