Conditional limit theorems for ordered random walks

2009/07/16 by Denis Denisov, Denisov, D., Vitali Wachtel +1 · 3 citations
Computer Science · Mathematics · #60F17(Secondary) #60G50 (Primary) 60G40 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0907.2854

openalex publication_date 2009/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the optimal moment assumptions for the construction of the conditional random walk and generalise the limit theorem for this conditional process.

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• Limit theorems for Markov walks conditioned to stay positive in the α-stable regime under a spectral gap assumption
• Random walks in Weyl chambers
• Discrete harmonic polynomials in multidimensional orthants

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