131 citations · 255 across the 21 of their papers we have counts for
21 papers
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…
The CR immersion into a sphere with the degenerate CR Gauss map
Wanke Yin, Yuan Yuan, Yuan Zhang
It is a classical problem in algebraic geometry to characterize the algebraic subvariety by using the Gauss map. In this note, we try to develop the analogue theory in CR geometry.…
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…
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…