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We consider a stochastic flow driven by a finite-dimensional Brownian
motion. We show that almost every realization of such a flow exhibits strong
statistical properties such as th...
On the concentration properties of Interacting particle processes
Concentration properties Feynman-Kac particle processes stochastic particle models
2011/9/1
Abstract: These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occup...
Path properties and regularity of affine processes on general state spaces
affine processes path properties regularity Markov semimartingales
2011/8/30
Abstract: We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the def...
Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
Finite size properties staggered $U_q[sl(2|1)]$ superspin chains
2011/3/2
Based on the exact solution of the eigenvalue problem for the Uq[sl(2|1)] vertex model
built from alternating 3-dimensional fundamental and dual representations by means of the
algebraic Bethe ansat...
Connectivity properties of random interlacement and intersection of random walks
Random interlacement random walk intersection of random walks capacity
2011/2/24
We consider the interlacement Poisson point process on the space of doubly-infinite Zd-valued
trajectories modulo time shift, tending to infinity at positive and negative infinite times. The set of v...
The local properties of the Markov processes of Ornstein-Uhlenbeck type
local time Markov process of Ornstein-Uhlenbeck type L´ evy process
2010/12/6
We prove the existence of a local time, the continuity of the local time about t, and the regular property for a.e. x ∈ R of a Ornstein-Uhlenbeck type {Xt, t ∈ R+} driven by a general L´evy proc...
Quasi-randomness of graph balanced cut properties
Quasi-randomness graph balanced cut properties
2010/12/6
Quasi-random graphs can be informally described as graphs whose edge distribution closely
resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster
proved the fol...