The lower tail of the random minimum spanning tree.
The outer-distance of nodes in random trees.
The probability of a successful allocation of ball groups by boxes.
The probability of the triangle inequality in probabilistic metric squares.
The shape of a typical boxed plane partition.
The "Thirty-seven Percent Rule" and the secretary problem with relative ranks
We revisit the problem of selecting an item from n choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first k items and then select the first subsequent item that ranks lower than the l-th lowest-ranked item among the first k. We prove that the optimal rule has k ~ n/e, as in the classical secretary problem where our sole objective is to select the item of lowest rank;...
The two uniform infinite quadrangulations of the plane have the same law
We prove that the uniform infinite random quadrangulations defined respectively by Chassaing–Durhuus and Krikun have the same distribution.
Tree-valued Markov chains derived from Galton-Watson processes
Two game-set inequalities.
Two-stage allocations and the double -function.
Uniform bounds for exponential moment of maximum of a Dyck path.
Using Lovász local lemma in the space of random injections.
Wahrscheinlichkeits- und Wettbegriff.
What was Nicolo Tartaglia doing in the night to Ash Wednesday of the year 1523 in Verona. (Was machte Nicolo Tartaglia in der Nacht zum Aschermittwoch des Jahres 1523 in Verona.)
Where the typical set partitions meet and join.
Zero-one laws for graphs with edge probabilities decaying with distance. Part I
Let Gₙ be the random graph on [n] = 1,...,n with the possible edge i,j having probability for j ≠ i, i+1, i-1 with α ∈ (0,1) irrational. We prove that the zero-one law (for first order logic) holds..
Асимптотика случайных разбиений множеств
Асимптотическая нормальность в схеме конечно-зависимого размещения частиц по ячейкам
Асимптотическая нормальность некоторых величин, связанных с цикловой структурой случайных подстановок
Вероятностный аналог задачи о центре графа