Ulam’s problemand Hammersley’s process
نویسنده
چکیده
Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1, . . . , n, for the uniform distribution on the set of permutations. Hammersley’s interacting particle process, implicit in Hammersley (1972), has been used in Aldous and Diaconis (1995) to provide a “soft” hydrodynamical argument for proving that limn→∞ ELn/ √ n = 2. We show in this note that the latter result is in fact an immediate consequence of properties of a random 2-dimensional signed measure, associated with Hammersley’s process. MSC 2000 subject classifications. Primary: 60C05,60K35, secondary 60F05.
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