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A random walk on image patches
image patches di usion maps Laplacian eigenmaps graph Laplacian
2011/7/19
In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time se...
Loss-sensitive Training of Probabilistic Conditional Random Fields
Loss-sensitive Training Probabilistic Conditional Random Fields
2011/7/19
We consider the problem of training probabilistic conditional random fields (CRFs) in the context of a task where performance is measured using a specific loss function. While maximum likelihood is th...
Sharp oracle inequalities and slope heuristic for specification probabilities estimation in general random fields
Sharp oracle inequalities slope heuristic specification probabilities estimation
2011/7/5
We provide new methods for estimation of the one-point specification probabilities in general discrete random fields.
Branching diffusions, superdiffusions and random media
spatial branching processes branching diffusions measure-valued processes superprocesses catalytic branching Law of Large Numbers
2009/5/18
Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinea...
On exchangeable random variables and the statistics of large graphs and hypergraphs
random variables large graphs large hypergraphs
2009/5/18
In this survey we recall the basic results of the theory of exchangeable laws, and then explain the probabilistic versions of various interesting questions from graph and hypergraph theory that their ...
On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks
Probabilities Wienertest Paley-Zygmund inequality
2009/5/4
We consider a continuous time random walk on the d-dimensional lattice Zd: the jump rates are time dependent, but symmetric and strongly elliptic with ellipticity constants independent of time. We inv...
A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment
random walk in random environment RWRE law of large numbers
2009/4/29
We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general...
Geodesics and Recurrence of Random Walks in Disordered Systems
Random environment with stationary conductances Geodesicsin in first-passage percolation model Recurrence and transience
2009/4/29
In a first-passage percolation model on the square lattice $Z^2$, if the passage times are independent then the number of geodesics is either $0$ or $+infty$. If the passage times are stationary, ergo...
Recurrent Graphs where Two Independent Random Walks Collide Finitely Often
Random walk Comb lattice collisions
2009/4/28
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from $Z^2$ by rem...
A relation between dimension of the harmonic measure，entropy and drift for a random walk on a hyperbolic space
harmonic measure entropy drift hyperbolic space
2009/3/19
We establish in this paper an exact formula which links the dimension of the harmonic measure, the asymptotic entropy and the rate of escape for a random walk on a discrete subgroup of the isometry gr...