, ? n,j?1 already determined, with some maximum max(? n1 , n} a value v is chosen uniformly at random from [n] \ {? n1 , . . . , ? n,j?1 }. If v < r ? let ? nj = r ? ?1 , if v > r u let ? nj = r u +1 , and if r ? < v < r u let ? nj = v. The sampled value v is replaced each time v breaks the last upper or lower record In n steps the increasing sequences , r u ) are shuffled with other elements of [n]. It is intiutively clear and not hard to show that, as n becomes large, n ?1 rec) will converge in S to (? k ) This is just because sampling from large finite sets will have nearly the same effect as independent uniform choices from [0, 1]. Apparently, from the viewpoint of statistical theory of extremes the sequence (X n ) is rather exotic, as it is chosen just to simulate desired behaviour of records, This differs general P (?,?) from the uniform distribution P (1,1) , when 'injecting' some extrinsic (? k ) is not at all necessary since the uniform sample (W n ) supplies automatically appropriate record values, so (X n ) d = (W n ). Still, in the case of integer parameters there is a simpler way to produce appropriate (X n ) from a sequence of uniforms, as parallels the construction of permutations in Proposition 3
, Riffle shuffles, cycles, and descents, Combinatorica, vol.94, issue.1, pp.15-26, 1995.
DOI : 10.1007/BF01294457
, Distribution-free tests in time-series based on the breaking of records, J. R. Stat. Soc. Ser. B, vol.16, pp.1-22, 1954.
, A Stochastic Game of Optimal Stopping and Order Selection, The Annals of Applied Probability, vol.5, issue.1, pp.310-321, 1995.
DOI : 10.1214/aoap/1177004842
, Coherent random permutations and the boundary problem for the graph of zigzag diagrams, Int. Math. Res. Notes Article ID, vol.39, p.51968, 2006.
, The boundary of the Eulerian number triangle, Moscow Math. J, vol.6, pp.461-475, 2006.
, Exchangeable Gibbs partitions and Stirling triangles, Zapiski POMI (St, Petersburg Dept. Steklov Math. Inst.) J. Math. Sci, vol.325, issue.138, pp.82-105, 2005.
DOI : 10.1007/s10958-006-0335-z
URL : http://arxiv.org/abs/math/0412494
, Records, permutations and greatest convex minorants, Math. Proc. Camb, pp.169-177, 1989.
DOI : 10.1214/aop/1176993450
, Record sequences and their applications, Handbook of StatisticsStochastic Processes: Theory and Methods, pp.277-308, 1999.
, Theory of rank tests, 1998.
, Sharp Inequalities for Optimal Stopping with Rewards Based on Ranks, The Annals of Applied Probability, vol.2, issue.2, pp.503-517, 1992.
DOI : 10.1214/aoap/1177005713
, On the number of consecutive successes in Bernoulli trials, 2006.
, Subordinators and the actions of permutations with quasi-invariant measure, Journal of Mathematical Sciences, vol.262, issue.23, pp.4094-4117, 1997.
DOI : 10.1007/BF02355805
, Stick breaking process generated by virtual permutations with Ewens distribution, Journal of Mathematical Sciences, vol.22, issue.23, pp.4082-4093, 1997.
DOI : 10.1007/BF02355804
, Harmonic analysis on the infinite symmetric group, Inventiones mathematicae, vol.55, issue.3, pp.316-773, 1993.
DOI : 10.1007/s00222-004-0381-4
, Riffle shuffles and their associated dynamical systems, Journal of Theoretical Probability, vol.12, issue.4, pp.903-932, 1999.
DOI : 10.1023/A:1021636902356
, Analytic variations on bucket selection and sorting, Acta Informatica, vol.36, issue.9-10, pp.735-760, 2000.
DOI : 10.1007/s002360050173
URL : https://hal.archives-ouvertes.fr/inria-00073290
, An extension of de Finetti's theorem, Advances in Applied Probability, vol.10, issue.02, pp.268-270, 1978.
DOI : 10.1007/BF00534783
, Combinatorial stochastic processes, Lecture Notes Math, vol.1875, 2006.
, Adventures in stochastic processes, 1992.
DOI : 10.1007/978-1-4612-0387-2