Related papers: Extremes of geometric variables with applications …
Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.
We consider a subcritical Galton--Watson tree conditioned on having $n$ vertices with outdegree in a fixed set $\Omega$. Under mild regularity assumptions we prove various limits related to the maximal offspring of a vertex as $n$ tends to…
In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal…
Let $(X_{n,i})_{1\le i\le n,n\in\mathbb{N}}$ be a triangular array of row-wise stationary $\mathbb{R}^d$-valued random variables. We use a "blocks method" to define clusters of extreme values: the rows of $(X_{n,i})$ are divided into $m_n$…
We review the question of the extreme values attained by a random process. We relate it to level crossings either to one boundary (first-passage problems) and two boundaries (escape problems). The extremes studied are the maximum, the…
A curious connection exists between the theory of optimal stopping for independent random variables, and branching processes. In particular, for the branching process $Z_n$ with offspring distribution $Y$, there exists a random variable $X$…
The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general preferences, weakening the assumptions of the known results…
We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of…
We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…
We study a new family of random variables, that each arise as the distribution of the maximum or minimum of a random number $N$ of i.i.d.~random variables $X_1,X_2,\ldots,X_N$, each distributed as a variable $X$ with support on $[0,1]$. The…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
In this article, we consider a branching random walk on the real-line where displacements coming from the same parent have jointly regularly varying tails. The genealogical structure is assumed to be a supercritical Galton-Watson tree,…
We consider extremal processes and random walks generated by heavy-tailed random vectors taking values in $\mathbb{R}^d$ endowed with the $\ell_p$ metric. We establish limit theorems for the associated paths in the triangular array setting…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
We obtain almost sure limit theorems for partial maxima of norms of a sequence of Banach-valued Gaussian random variables.
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
Extreme economic outcomes are not shaped by tails alone. They are also shaped by unequal access to opportunities. This paper develops a theory of heterogeneous extremes by taking the distribution of opportunity access as the object of…
We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…