Cancelations in random sums

Series: 
ACO Student Seminar
Friday, November 16, 2018 - 1:05pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Math, University of Michigan
,  
Organizer: 

Consider a linear combination of independent identically distributed random variables $X_1, . . . , X_n$ with fixed weights $a_1, . . . a_n$. If the random variablesare continuous, the sum is almost surely non-zero. However, for discrete random variables an exact cancelation may occur with a positive probability. Thisprobability depends on the arithmetic nature of the sequence $a_1, . . . a_n$. We will discuss how to measure the relevant arithmetic properties and how to evaluate the probability of the exact and approximate cancelation.