Monotonicity for excited random walk in high dimensions

2008/03/13 by Remco van der Hofstad, van der Hofstad, Remco, Mark Holmes +1
Mathematics · Biochemistry, Genetics and Molecular Biology · #Stochastic processes and statistical mechanics #Diffusion and Search Dynamics #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.0803.1881

Abstract

We prove that the drift θ(d,β) for excited random walk in dimension d is monotone in the excitement parameter β∈[0, 1], when d≥ 9.

Citations

• Excited random walk in three dimensions has positive speed

Related

• On strict monotonicity of the speed for excited random walks in one dimension
• Some results on regularity and monotonicity of the speed for excited\n random walk in low dimensions
• Strict monotonicity properties in one-dimensional excited random walks
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• A note on transience of generalized many-dimensional excited random walks