Abstract
Consider the set of finite words on a totally ordered alphabet with two letters. We prove that the distribution of the length of the standard right factor of a random Lyndon word with length n, divided by n, converges to u(dx) = ½δ1(dx + ½1(0,1)(x)dx when n goes to infinity. The convergence of all moments follows. This paper thus completes the results of [2], in which the limit of the first moment is given.
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