Limit theorems for the least common multiple of random integer sets

Seminarium: 
Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca: 
Alexander Marynych (Taras Shevchenko National University of Kyiv)
Data spotkania seminaryjnego: 
czwartek, 4. Czerwiec 2020 - 12:15
Sala: 
Zoom, kontakt: michal.krawiec@math.uni.wroc.pl
Opis: 
In my talk I shall consider two models for random integer sets and derive limit theorems for the least common multiple of their elements. In the first model a random set is defined by the Bernoulli sieving of $\{1,2,\ldots,n\}$ with a constant rate $\theta\in(0,1)$. In the second model the set consists of k independent uniform random variables on $\{1,2,3,\ldots,n\}$.