Related papers: Fixed points with finite mean of the smoothing tra…

Consider a heavy-tailed branching process (denoted by $Z_{n}$) in random environments, under the condition which infers that $\mathbb{E}\log m(\xi_{0})=\infty$. We show that (1) there exists no proper $c_{n}$ such that $\{Z_{n}/c_{n}\}$ has…

The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to…

In this paper, we first introduce and study the notion of random Chebyshev centers. Further, based on the recently developed theory of stable sets, we introduce the notion of random complete normal structure so that we can prove the two…

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 depending on whether the jumps of the standard random walk are…

We investigate moment sequences of probability measures on $E\subset\mathbb{R}$ under constraints of certain moments being fixed. This corresponds to studying sections of $n$-th moment spaces, i.e. the spaces of moment sequences of order…

We call $i$ a fixed point of a given sequence if the value of that sequence at the $i$-th position coincides with $i$. Here, we enumerate fixed points in the class of restricted growth sequences. The counting process is conducted by…

Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables, and $\eta$ be a counting random variable independent of this sequence. In addition, let $S_0:=0$ and $S_n:=\xi_1+\xi_2+\cdots+\xi_n$ for $n\geqslant1$. We consider…

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…

In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…

We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can…

This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal constants in the Khintchine inequality for random vectors…

For two collections of nonnegative and suitably normalised weights $\W=(\W_j)$ and $\V=(\V_{n,k})$, a probability distribution on the set of partitions of the set $\{1,...,n\}$ is defined by assigning to a generic partition $\{A_j, j\leq…

When the distribution of a random (N) sum of independent copies of a r.v X is of the same type as that of X we say that X is N-sum stable. In this paper we consider a generalization of stability of geometric sums by studying distributions…

Motivated by the randomized version of the classical Bolzano--Weierstrass theorem, in this paper we first introduce the notion of a random sequentially compact set in a random normed module and develop the related theory systematically.…

In this paper, we study a transient spatially inhomogeneous random walk with asymptotically zero drifts on the lattice of the positive half line. We give criteria for the finiteness of the number of points having exactly the same local time…

Let $Z_{n,}n=0,1,...,$ be a branching process evolving in the random environment generated by a sequence of iid generating functions $% f_{0}(s),f_{1}(s),...,$ and let $S_{0}=0,S_{k}=X_{1}+...+X_{k},k\geq 1,$ be the associated random walk…

Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…

We study branching random walk on $\mathbb{Z}$ in a bounded i.i.d. random environment. For this process, we prove that, for almost every realization of the environment, the distributions of the maximally displaced particle (re-centered…

A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…

Based on the recently developed theory of random sequential compactness, we prove the random Kakutani fixed point theorem in random normed modules: if G is a random sequentially compact L0-convex subset of a random normed module, then every…