Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers
del Junco, A. ; Steele, J. Michael
Ann. Probab., Tome 7 (1979) no. 6, p. 267-275 / Harvested from Project Euclid
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The analogue of Hammersley's theorem on the length of the longest monotonic subsequence of independent, identically, and continuously distributed random variables is obtained for the pseudorandom van der Corput sequence. In this case there is no limit but the precise limits superior and inferior are determined. The constants obtained are closely related to those established in the independent case by Logan and Shepp, and Vershik and Kerov.
Publié le : 1979-04-14
Classification:  Van der Corput sequence,  monotonic subsequence,  60C05,  65C10 
@article{1176995087,
     author = {del Junco, A. and Steele, J. Michael},
     title = {Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers},
     journal = {Ann. Probab.},
     volume = {7},
     number = {6},
     year = {1979},
     pages = { 267-275},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995087}
}

del Junco, A.; Steele, J. Michael. Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers. Ann. Probab., Tome 7 (1979) no. 6, pp.  267-275. http://gdmltest.u-ga.fr/item/1176995087/