Conditional limit theorems for ordered random walks
By Denis Denisov, Vitali Wachtel. 2009
49 citations recorded by the source corpus.
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 proposed by Eichelsbacher and Koenig, and generalise the limit theorem for this conditional process.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/684fa00d069e9e7c29f2d666de0e75e997150705
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Citations in the corpus
- Random walks in cones (2011, background): “It is shown in [16] that all the statements in Theorems 1 and 3 remain valid under the condition E|X|d−1 <∞.”
- Random walks in the quarter plane, discrete harmonic functions and conformal mappings (2013, background): “Random processes conditioned on staying in cones of Z arouse a great interest in the mathematical community, as they appear in several distinct domains: quantum random walks [3, 5], random matrices [11], non-colliding random walks [8, 9, 12], etc.”