#### Filter Results:

- Full text PDF available (38)

#### Publication Year

1961

2016

- This year (0)
- Last 5 years (3)
- Last 10 years (12)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Harry Kesten, H. D. Kesten
- 2004

We prove the statement in the title of the paper.

- Harry Kesten
- 2004

Let Pp be the probability measure on the configurations of occupied and vacant vertices of a two-dimensional graph N, under which all vertices are independently occupied (respectively vacant) with probability p (respectively l p ) . Let p~ be the critical probability for this system and W the occupied cluster of some fixed vertex w o. We show that for many… (More)

Abstract Shnerb et al. (2000), (2001) studied the following system of interacting particles on Z: There are two kinds of particles, called A-particles and B-particles. The A-particles perform continuous time simple random walks, independently of each other. The jumprate of each A-particle is DA. The B-particles perform continuous time simple random walks… (More)

We consider the motion of a particle in a weak mean zero random force field F, which depends on the position, x(t), and the velocity, v(t) = 2(0. The equation of motion is 2(0 = ef(x( t ) , v(t), 0~), where x( ') and v(-) take values in R d, d > 3, and co ranges over some probability space. We show, under suitable mixing and moment conditions on F, that as… (More)

- Harry Kesten
- 1990

We prove that the critical probability for bond or site percolation on Z is asymptotically equal to 1/(2d) as d → ∞. If the probability of a bond (respectively site) to be occupied is γ/(2d) with γ > 1, then for the bond model the percolation probability converges as d → ∞ to the strictly positive solution y(γ) of the equation y = 1− exp(−γy). In the site… (More)

We show under some specific conditions that the formal diffusion approximation for the motion of a particle in a random velocity field is valid.

We consider critical site percolation on the triangular lattice, that is, we choose X(v) = 0 or 1 with probability 1/2 each, independently for all vertices v of the triangular lattice. We say that a word (ξ1, ξ2, . . . ) ∈ {0, 1}N is seen in the percolation configuration if there exists a selfavoiding path (v1, v2, . . . ) on the triangular lattice with… (More)

We consider the following interacting particle system: There is a “gas” of particles, each of which performs a continuous-time simple random walk on Z, with jump rate DA. These particles are called A-particles and move independently of each other. They are regarded as individuals who are ignorant of a rumor or are healthy. We assume that we start the system… (More)

The uniform spanning forest (USF) in Z is the weak limit of random, uniformly chosen, spanning trees in [−n,n]. Pemantle (1991) proved that the USF consists a.s. of a single tree if and only if d ≤ 4. We prove that any two components of the USF in Z are adjacent a.s. if 5 ≤ d ≤ 8, but not if d ≥ 9. More generally, let N(x, y) be the minimum number of edges… (More)

- Harry Kesten
- Microsurveys in Discrete Probability
- 1997