Coding of Poisson random sets: large derivations

Date

Jun 19, 2019

Time

5:00 PM - 6:00 PM

Speaker

Prof. Mikhail A. Lifshits

Affiliation

St. Petersburg State Univerity, Russland

Series

TUD Dresdner Mathematisches Seminar

Language

de

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. René Schilling, Dr. Carina Geldhauser

Description

Consider a random set (or "picture") in the unit cube of d-dimensional Euclidean space as a union of balls centered at points of a Poissonian random field and having i.i.d. radii. Let K be the minimal number of balls needed to reproduce the picture.We study large deviation probabilities for K and prove in some cases that for large n ln P( K > n) − A n ln n where the constant A may explicitly depend on dimension, on the distribution of radii, and on the norm under consideration. In many cases the problem of finding the value of A remains open although some upper and lower bounds are available. This asymptotics has natural corollaries in high dimensional quantization problems.

Dresdner Mathematisches Seminar

Last modified: Jun 18, 2019, 11:57:38 AM