Random walk on random walks: higher dimensions
Copyright policy )Random walk on random walks: higher dimensions
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition kernels without the assumption of uniform ellipticity or nearest-neighbour jumps. Specifically, we obtain a strong law of large numbers, a functional central limit theorem and large deviation estimates for the position of the random walker under the annealed law in a high density regime. The main obstacle is the intrinsic lack of monotonicity in higher-dimensional, non-nearest neighbour settings. Here we develop more general renormalization and renewal schemes that allow us to overcome this issue. As a second application of our methods, we provide an alternative proof of the ballistic behaviour of the front of (the discrete-time version of) the infection model introduced in [23].
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Strong limit theorems, dynamic random environment, Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics, strong law of large numbers, central limit theorem, 82B41, Random walk, large deviations, 510, renormalization, random walk, FOS: Mathematics, Secondary 82B41, Processes in random environments, Interacting particle systems in time-dependent statistical mechanics, large deviation bound, ddc:510, Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics, dynamical random environment, functional central limit theorem, law of large num- bers, Probability (math.PR), article, Random walk -- dynamic random environment -- law of large numbers -- central limit theorem -- large deviations -- renormalization -- regeneration, law of large numbers, Interacting random processes; statistical mechanics type models; percolation theory, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], renormalization regeneration times, 60K37, 60K35, regeneration, 60F15, 82C22, 82C44, Mathematics - Probability, regeneration AMS MSC 2010: Primary 60F15
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Strong limit theorems, dynamic random environment, Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics, strong law of large numbers, central limit theorem, 82B41, Random walk, large deviations, 510, renormalization, random walk, FOS: Mathematics, Secondary 82B41, Processes in random environments, Interacting particle systems in time-dependent statistical mechanics, large deviation bound, ddc:510, Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics, dynamical random environment, functional central limit theorem, law of large num- bers, Probability (math.PR), article, Random walk -- dynamic random environment -- law of large numbers -- central limit theorem -- large deviations -- renormalization -- regeneration, law of large numbers, Interacting random processes; statistical mechanics type models; percolation theory, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], renormalization regeneration times, 60K37, 60K35, regeneration, 60F15, 82C22, 82C44, Mathematics - Probability, regeneration AMS MSC 2010: Primary 60F15
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