Seminario di probabilità e statistica matematica

Aula di Consiglio, Dipartimento di Matematica Guido Castelnuovo Lunedì 3 aprile, ore 16:00

Mauro Piccioni (Università di Roma La Sapienza)

terrà una conferenza dal titolo:

How it happened (to me) to meet ?

Summary: The function ? was defined by Minkowski with the purpose of mapping quadratic irrationals bijectively onto the rationals of (0,1) (in addition, it maps the rationals onto the dyadic rationals). It has remarkable self-similarity properties and it maps (increasingly) the interval [0,1] into itself, with an almost everywhere vanishing derivative. For this reason it has been named the slippery devil’s staircase (to distinguish it from the Cantor set distribution function, which, not being strictly increasing, is not slippery!). In the talk we will obtain it as the equilibrium law of a random walk on the homogeneous space (H,PSL_2(Z)) where H is the upper half-plane in the complex plane and PSL_2(Z) is the modular group. The random walk walk drifts towards the real line with a limit in law X whose image under the function |x|v|x|^{-1} has distribution function ?. In proving this, the characterization of a ?-distributed random variable Y in term of its continued fraction expansion is also obtained. This is a joint work with Gerard Letac.

Tutti gli interessati sono invitati a partecipare. Per informazioni rivolgersi a piccioni@mat.uniroma1.it

---------------------------------------------------------------- Gustavo Posta

Dipartimento di Matematica Università di Roma "la Sapienza" P.le A. Moro 2, 00185 Roma Italy

web: http://www1.mat.uniroma1.it/~posta e-mail: gustavo.posta@uniroma1.it phone: +39-06-4991-4969 ------------------------------------------------------------------