The cut-off phenomenon for random reflections
Porod, Ursula
Ann. Probab., Tome 24 (1996) no. 2, p. 74-96 / Harvested from Project Euclid
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For many random walks on "sufficiently large" finite groups the so-called cut-off phenomenon occurs: roughly stated, there exists a number $k_0$ , depending on the size of the group, such that $k_0$ steps are necessary and sufficient for the random walk to closely approximate uniformity. As a first example on a continuous group, Rosenthal recently proved the occurrence of this cut-off phenomenon for a specific random walk on $SO(N)$. Here we present and [for the case of $O(N)$] prove results for random walks on $O(N), U(N)$ and $Sp(N)$, where the one-step distribution is a suitable probability measure concentrated on reflections. In all three cases the cut-off phenomenon occurs at $k_0 = 1/2 N\log N$.
Publié le : 1996-01-14
Classification:  Random walk,  reflection,  cut-off phenomenon,  Fourier analysis,  60J15,  60B15 
@article{1042644708,
     author = {Porod, Ursula},
     title = {The cut-off phenomenon for random reflections},
     journal = {Ann. Probab.},
     volume = {24},
     number = {2},
     year = {1996},
     pages = { 74-96},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1042644708}
}

Porod, Ursula. The cut-off phenomenon for random reflections. Ann. Probab., Tome 24 (1996) no. 2, pp.  74-96. http://gdmltest.u-ga.fr/item/1042644708/