Academic literature on the topic 'Random walks in symmetric exclusion processes'

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Journal articles on the topic "Random walks in symmetric exclusion processes"

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Oliveira, Roberto Imbuzeiro. "Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk." Annals of Probability 41, no. 2 (March 2013): 871–913. http://dx.doi.org/10.1214/11-aop714.

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van Ginkel, Bart, and Frank Redig. "Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold." Journal of Statistical Physics 178, no. 1 (November 11, 2019): 75–116. http://dx.doi.org/10.1007/s10955-019-02420-2.

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Abstract We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the solution of the heat equation on the manifold.
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Feldman, Raisa Epstein. "Autoregressive processes and first-hit probabilities for randomized random walks." Journal of Applied Probability 28, no. 2 (June 1991): 347–59. http://dx.doi.org/10.2307/3214871.

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We find the first-hit distributions of symmetric randomized random walks on ℝ with exponential lifetime using prediction formulas for Gaussian stationary autoregressive processes, associated with the random walks.
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Feldman, Raisa Epstein. "Autoregressive processes and first-hit probabilities for randomized random walks." Journal of Applied Probability 28, no. 02 (June 1991): 347–59. http://dx.doi.org/10.1017/s0021900200039735.

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We find the first-hit distributions of symmetric randomized random walks on ℝ with exponential lifetime using prediction formulas for Gaussian stationary autoregressive processes, associated with the random walks.
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Greven, Andreas. "Symmetric exclusion on random sets and a related problem for random walks in random environment." Probability Theory and Related Fields 85, no. 3 (September 1990): 307–64. http://dx.doi.org/10.1007/bf01193942.

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YANG, ZHIHUI. "LARGE DEVIATION ASYMPTOTICS FOR RANDOM-WALK TYPE PERTURBATIONS." Stochastics and Dynamics 07, no. 01 (March 2007): 75–89. http://dx.doi.org/10.1142/s0219493707001950.

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Symmetric random walks can be arranged to converge to a Wiener process in the area of normal deviation. However, random walks and Wiener processes have, in general, different asymptotics of the large deviation probabilities. The action functionals for random-walks and Wiener processes are compared in this paper. The correction term is calculated. Exit problem and stochastic resonance for random-walk-type perturbation are also considered and compared with the white-noise-type perturbation.
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Hilário, Marcelo R., Daniel Kious, and Augusto Teixeira. "Random Walk on the Simple Symmetric Exclusion Process." Communications in Mathematical Physics 379, no. 1 (August 26, 2020): 61–101. http://dx.doi.org/10.1007/s00220-020-03833-x.

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Abstract We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole, so that its asymptotic behavior is expected to depend on the density $$\rho \in [0, 1]$$ ρ ∈ [ 0 , 1 ] of the underlying SSEP. Our first result is a law of large numbers (LLN) for the random walker for all densities $$\rho $$ ρ except for at most two values $$\rho _-, \rho _+ \in [0, 1]$$ ρ - , ρ + ∈ [ 0 , 1 ] . The asymptotic speed we obtain in our LLN is a monotone function of $$\rho $$ ρ . Also, $$\rho _-$$ ρ - and $$\rho _+$$ ρ + are characterized as the two points at which the speed may jump to (or from) zero. Furthermore, for all the values of densities where the random walk experiences a non-zero speed, we can prove that it satisfies a functional central limit theorem (CLT). For the special case in which the density is 1/2 and the jump distribution on an empty site and on an occupied site are symmetric to each other, we prove a LLN with zero limiting speed. We also prove similar LLN and CLT results for a different environment, given by a family of independent simple symmetric random walks in equilibrium.
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Schulz, J. H. P., A. B. Kolomeisky, and E. Frey. "Current reversal and exclusion processes with history-dependent random walks." EPL (Europhysics Letters) 95, no. 3 (July 19, 2011): 30004. http://dx.doi.org/10.1209/0295-5075/95/30004.

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Faggionato, Alessandra. "Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit." Electronic Journal of Probability 13 (2008): 2217–47. http://dx.doi.org/10.1214/ejp.v13-591.

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Agbor, A., S. Molchanov, and B. Vainberg. "Global limit theorems on the convergence of multidimensional random walks to stable processes." Stochastics and Dynamics 15, no. 03 (May 22, 2015): 1550024. http://dx.doi.org/10.1142/s0219493715500240.

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Symmetric heavily tailed random walks on Zd, d ≥ 1, are considered. Under appropriate regularity conditions on the tails of the jump distributions, global (i.e. uniform in x, t, ∣x∣ + t → ∞,) asymptotic behavior of the transition probability p(t, 0, x) is obtained. The examples indicate that the regularity conditions are essential.
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Book chapters on the topic "Random walks in symmetric exclusion processes"

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Marcus, Michael B., and Jay Rosen. "Moment Generating Functions for Local Times of Symmetric Markov Processes and Random Walks." In Probability in Banach Spaces, 8:, 364–76. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0367-4_25.

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