24 citations · 99 across the 51 of their papers we have counts for
4 papers · 1 filter
How long is the convex minorant of a one-dimensional random walk?
Gerold Alsmeyer, Zakhar Kabluchko, Alexander Marynych +1
We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending…
Sieving random iterative function systems
Alexander Marynych, Ilya Molchanov
It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) proc…
Random walks in a strongly sparse random environment
Dariusz Buraczewski, Piotr Dyszewski, Alexander Iksanov +1
The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depe…
On the least common multiple of several random integers
Alin Bostan, Alexander Marynych, Kilian Raschel
Let denote the least common multiple of independent random integers uniformly chosen in . In this note, using a purely probabilistic approach, we de…