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Asymptotic results for the number of Wagner's solutions to a generalised birthday problem

Alexey Lindo (Institutionen för matematiska vetenskaper, matematisk statistik) ; Serik Sagitov (Institutionen för matematiska vetenskaper, matematisk statistik)
Statistics and Probability Letters (0167-7152). Vol. 107 (2015), p. 356-361.
[Artikel, refereegranskad vetenskaplig]

We study two functionals of a random matrix A with independent elements uniformly distributed over the cyclic group of integers {0, 1, . . ., M-1} modulo M. One of them, V0(A) with mean μ, gives the total number of solutions for a generalised birthday problem, and the other, W(A) with mean λ, gives the number of solutions detected by Wagner's tree based algorithm.We establish two limit theorems. Theorem 2.1 describes an asymptotical behaviour of the ratio λ/μ as M→∞. Theorem 2.2 gives bounds for the total variation distance between Poisson distribution and distributions of V0 and W.

Nyckelord: Chen-Stein method , Functionals of random matrices



Denna post skapades 2015-10-26. Senast ändrad 2016-01-08.
CPL Pubid: 224779

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematisk statistik

Chalmers infrastruktur