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We propose a novel statistical method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect object...
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect obje...
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect obje...
Lipschitz percolation     percolation  Lipschitz embedding  random surface       font style='font-size:12px;'> 2010/2/24
We prove the existence of a (random) Lipschitz function F: Zd-1 → Z+ such that, for every x∈ Zd-1, the site (x,F(x)) is open in a site percolation process on Zd. The Lipschitz constant may be taken to...
A Note on Percolation of Poisson Sticks     Percolation  Poisson Sticks       font style='font-size:12px;'> 2009/9/17
A Note on Percolation of Poisson Sticks。
This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on $Z^d$ and more generally on transitive graphs. For iid percolation o...
A comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results co...
We give a counterexample to a conjecture of Hammersley and Welsh (1965) about the convexity of the time constant in first-passage percolation, as a functional on the space of distribution functions. T...
Percolation Dimension of Brownian Motion in R^3     Brownian Motion  Percolation Dimension       font style='font-size:12px;'> 2009/5/8
Let $B(t)$ be a Brownian motion in $R^3$. A {it subpath} of the Brownian path $B[0,1]$ is a continuous curve $gamma(t)$, where $gamma[0,1] subseteq B[0,1]$ , $gamma(0) = B(0)$, and $gamma(1) = B(1)$. ...
A Percolation Formula     SLE  Cardy  conformal invariance       font style='font-size:12px;'> 2009/5/4
Let A be an arc on the boundary of the unit disk U. We prove an asymptotic formula for the probability that there is a percolation cluster K for critical site percolation on the triangular grid in U w...
Some two-dimensional finite energy percolation processes     percolation  uniform finite energy  coexistence       font style='font-size:12px;'> 2009/4/29
Some examples of translation invariant site percolation processes on the $Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the p...
On Long Range Percolation with Heavy Tails     Long range percolation  truncation  slab percolation       font style='font-size:12px;'> 2009/4/28
Consider independent long range percolation on $mathbf{Z}^d$, $dgeq 2$, where edges of length $n$ are open with probability $p_n$. We show that if $limsup_{ntoinfty}p_n>0,$ then there exists an i...
Random Walk Attracted by Percolation Clusters      subcritical percolation  subdiffusivity  reversibility  spectral gap       font style='font-size:12px;'> 2009/4/27
Starting with a percolation model in Zd in the subcritical regime, we consider a random walk described as follows: the probability of transition from x to y is proportional to some function f of the s...
We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the or...
Critical Exponents in Percolation via Lattice Animals     Percolation  lattice animals       font style='font-size:12px;'> 2009/4/24
We examine the percolation model on $mathbb{Z}^d$ by an approach involving lattice animals and their surface-area-to-volume ratio. For $beta in [0,2(d-1))$, let $f(beta)$ be the asymptotic exponential...

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