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On Infection Spreading And Competition Between Independent Random Walks
, 2003
"... We study the models of competition and spreading of infection for infinite systems of independent random walks. For the competition model, we investigate the question whether one of the spins prevails with probability one. For the infection spreading, we give su#cient conditions for recurrence a ..."
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We study the models of competition and spreading of infection for infinite systems of independent random walks. For the competition model, we investigate the question whether one of the spins prevails with probability one. For the infection spreading, we give su#cient conditions for recurrence
Occupation Time Limit Theorems For Independent Random Walks
, 1994
"... . We summarize many limit theorems for systems of independent simple random walks in Z. These theorems are classified into four classes: weak convergence, moderate deviations, large deviations and enormous deviations. A hierarchy of relations is pointed out and some open problems are posed. Extensio ..."
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Cited by 1 (1 self)
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. We summarize many limit theorems for systems of independent simple random walks in Z. These theorems are classified into four classes: weak convergence, moderate deviations, large deviations and enormous deviations. A hierarchy of relations is pointed out and some open problems are posed
Hitting times for independent random walks on Z^d
, 2004
"... We consider a system of asymmetric independent random walks on Z d, denoted by {ηt,t ∈ R}, stationary under the product Poisson measure νρ of marginal density ρ> 0. We fix a pattern A, an increasing local event, and denote by τ the hitting time of A. By using a Loss Network representation of our ..."
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Cited by 1 (0 self)
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We consider a system of asymmetric independent random walks on Z d, denoted by {ηt,t ∈ R}, stationary under the product Poisson measure νρ of marginal density ρ> 0. We fix a pattern A, an increasing local event, and denote by τ the hitting time of A. By using a Loss Network representation of our
Spacetime current process for independent random walks in one dimension
"... In a system made up of independent random walks, fluctuations of order n1/4 from the hydrodynamic limit come from particle current across characteristics. We show that a twoparameter spacetime particle current process converges to a twoparameter Gaussian process. These Gaussian processes also app ..."
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Cited by 6 (1 self)
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In a system made up of independent random walks, fluctuations of order n1/4 from the hydrodynamic limit come from particle current across characteristics. We show that a twoparameter spacetime particle current process converges to a twoparameter Gaussian process. These Gaussian processes also
On infection spreading and competition between independent random walks
 Electron. J. Probab. 9
, 2004
"... E l e c t r o n ..."
Hitting times for independent random walks ion Z^d
, 2004
"... We consider a system of asymmetric independent random walks on Z d, denoted by {ηt,t ∈ R}, stationary under the product Poisson measure νρ of marginal density ρ> 0. We fix a pattern A, an increasing local event, and denote by τ the hitting time of A. By using a Loss Network representation of our ..."
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We consider a system of asymmetric independent random walks on Z d, denoted by {ηt,t ∈ R}, stationary under the product Poisson measure νρ of marginal density ρ> 0. We fix a pattern A, an increasing local event, and denote by τ the hitting time of A. By using a Loss Network representation of our
Theory.. 'Related Fields 9 SpringerVerlag 1990 Large Deviations for Independent Random Walks*
"... Summary. We consider a system of independent random walks on 7/. Let r be the number of particles at x at time n, and let L,,(x) = ~o(X) +... + r be the total occupation time of x by time n. In this paper we study the large deviations of L.(0) L,(1). The behavior we find is much different from tha ..."
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Summary. We consider a system of independent random walks on 7/. Let r be the number of particles at x at time n, and let L,,(x) = ~o(X) +... + r be the total occupation time of x by time n. In this paper we study the large deviations of L.(0) L,(1). The behavior we find is much different from
First Occurrence Time of a Large Density Fluctuation for a System of Independent Random Walks
"... We obtain sharp asymptotics for the first time a "macroscopic" density fluctuation occurs in a system of independent simple symmetric random walks. Also, we show the convergence of the moments of the rescaled time by establishing tail estimates. ..."
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Cited by 2 (1 self)
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We obtain sharp asymptotics for the first time a "macroscopic" density fluctuation occurs in a system of independent simple symmetric random walks. Also, we show the convergence of the moments of the rescaled time by establishing tail estimates.
Results 1  10
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1,785,997