Abstract
LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV n overGF(q). A metric may be defined onX by letting
The nearest neighbor random walk onX starts at an initial fixed pointZ k ofX and, from wherever it finds itself, moves with the same probability to any of the points ofX at distance one from it. We analyze the rate of convergence of the nearest neighbor random walk onX to its stationary distribution. The argument involves lifting the process onX to a random walk onGL n(GF(q)) and using the Fourier transform andq-Hahn polynomials.
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D'Aristotile, A.J. The nearest neighbor random walk on subspaces of a vector space and rate of convergence. J Theor Probab 8, 321–346 (1995). https://doi.org/10.1007/BF02212882
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DOI: https://doi.org/10.1007/BF02212882