In the classical occupancy problem one puts balls in n boxes, and each ball is independently assigned to any fixed box with probability 1/ n . It is well known that, if we consider the random number T_n of balls required to have all the n boxes lled with at least one ball, the sequence (T_n/ n log n ) converges to 1 in probability. Here we present the large deviation principle associated to this convergence. We also discuss the use of the Gartner Ellis Theorem for the proof of some parts of this large deviation principle.

On The asymptotic behaviour of a sequences of random variables of interest in the classical occupancy problem

GIULIANO, RITA;
In corso di stampa

Abstract

In the classical occupancy problem one puts balls in n boxes, and each ball is independently assigned to any fixed box with probability 1/ n . It is well known that, if we consider the random number T_n of balls required to have all the n boxes lled with at least one ball, the sequence (T_n/ n log n ) converges to 1 in probability. Here we present the large deviation principle associated to this convergence. We also discuss the use of the Gartner Ellis Theorem for the proof of some parts of this large deviation principle.
In corso di stampa
Giuliano, Rita; Macci, C.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/159936
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact