%0 Generic %1 citeulike:84413 %A Marchand, Regine %A Azad, Elahe Z. %D 2004 %K lyndon word %T Limit law of the standard right factor of a random Lyndon word %U http://arxiv.org/abs/math.PR/0407016 %X Consider the set of finite words on a totally ordered alphabet with $q$ 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: $$\mu(dx)=\frac1q \delta_1(dx) + q-1q 1_0,1)(x)dx,$$ when $n$ goes to infinity. The convergence of all moments follows. This paper completes thus the results of Bassino, giving the asymptotics of the mean length of the standard right factor of a random Lyndon word with length $n$ in the case of a two letters alphabet.

@misc{citeulike:84413, abstract = {Consider the set of finite words on a totally ordered alphabet with $q$ 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: $$\mu(dx)=\frac1q \delta_{1}(dx) + \frac{q-1}q \mathbf{1}_{[0,1)}(x)dx,$$ when $n$ goes to infinity. The convergence of all moments follows. This paper completes thus the results of \cite{Bassino}, giving the asymptotics of the mean length of the standard right factor of a random Lyndon word with length $n$ in the case of a two letters alphabet.}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Marchand, Regine and Azad, Elahe Z.}, biburl = {https://www.bibsonomy.org/bibtex/25dfdaa4046190189e9dfcb60205236c9/a_olympia}, citeulike-article-id = {84413}, description = {citeulike}, eprint = {math.PR/0407016}, interhash = {1224b4a6ae6516d53422bdc63681e3dc}, intrahash = {5dfdaa4046190189e9dfcb60205236c9}, keywords = {lyndon word}, month = {July}, priority = {2}, timestamp = {2007-08-18T13:22:54.000+0200}, title = {Limit law of the standard right factor of a random Lyndon word}, url = {http://arxiv.org/abs/math.PR/0407016}, year = 2004 }