How long is the convex minorant of a one-dimensional random walk?

Seminarium: 
Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca: 
Alexander Marynych (Taras Shevchenko National University of Kyiv)
Data spotkania seminaryjnego: 
czwartek, 16. Styczeń 2020 - 12:15
Sala: 
602
Opis: 
In the talk I will prove several distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk. The proofs utilise a connection between convex minorants of random walks and uniform random permutations, that goes back to Sparre Andersen, Spitzer and Goldie, and which will also be discussed in details.