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A nontrivial constant c=0.29795219028 in one and three dimensional random walks

Majumdar, S (Universite Paris-Sud)
Monday 26 June 2006, 11:30-12:30

Seminar Room 1, Newton Institute


Two different random walk problems, one in one dimension and the other in three dimensions, seem to share a nontrivial constant whose numerical value is c=0.29795219028.. In the first problem, this constant shows up in the finite size correction to the expected maximum of a discrete-time random walk on a continuous line with unform jump density. In the second problem, this constant appears as the `Milne extrapolation length' in the expression for flux of discrete-time random walkers to a spherical trap in three dimensions. We prove why the same constant appears in the two problems and derive an exact analytical formula for this constant.


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