Abstract
We calculate the moments 〈t q〉, whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and 〈t q 〉 ~L τ (q) asL→∞, then we show that there is a phase transition atq=q c such that whenq<q c ,τ(g)=0, and forq>q c , τ(q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.
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Weiss, G.H., Havlin, S. & Matan, O. Properties of noninteger moments in a first passage time problem. J Stat Phys 55, 435–439 (1989). https://doi.org/10.1007/BF01042610
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DOI: https://doi.org/10.1007/BF01042610