## Asymptotics of the maximal radius of an $L^r$-optimal sequence of quantizers

 Title Asymptotics of the maximal radius of an ${L}^r$-optimal sequence of quantizers Publication Type Miscellaneous Year of Publication 2008 Authors Gilles Pagès, and Abass Sagna Abstract Let be a probability distribution on (equipped with an Euclidean norm). Let and assume is an (asymptotically) -optimal sequence of -quantizers. In this paper we investigate the asymptotic behavior of the maximal radius sequence induced by the sequence and defined to be for every , . We show that if is infinite, the maximal radius sequence goes to as goes to infinity. We then give the rate of convergence for two classes of distributions with unbounded support : distributions with exponential tails and distributions with polynomial tails.