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Optimal Bounds for the Variance of Self-Intersection Local Times
2016
International Journal of Stochastic Analysis
For aZd-valued random walk(Sn)n∈N0, letl(n,x)be its local time at the sitex∈Zd. Forα∈N, define theα-fold self-intersection local time asLn(α)≔∑xl(n,x)α. Also letLnSRW(α)be the corresponding quantities for the simple random walk inZd. Without imposing any moment conditions, we show that the variance of the self-intersection local time of any genuinelyd-dimensional random walk is bounded above by the corresponding quantity for the simple symmetric random walk; that
doi:10.1155/2016/5370627
fatcat:mfgejeukdfcfpfymrsqfgnfu2a