Related papers: Minimal supporting subtrees for the free energy of…
In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to zeta(3)=1/1^3+1/2^3+1/3^3+... as n goes to infinity. We consider…
In this paper, we investigate random walks in a family of small-world trees having an exponential degree distribution. First, we address a trapping problem, that is, a particular case of random walks with an immobile trap located at the…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
We study the thermodynamic properties of a semiflexible polymer confined inside strips of widths L<=9 defined on a square lattice. The polymer is modeled as a self-avoiding walk and a short range interaction between the monomers and the…
We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence…
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving…
Consider a collection of particles interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at unit separation. For a range of exponents corresponding to mild…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
We consider the random wetting transition on the Cayley tree, i.e. the problem of a directed polymer on the Cayley tree in the presence of random energies along the left-most bonds. In the pure case, there exists a first-order transition…
The rupture of a polymer chain maintained at temperature $T$ under fixed tension is prototypical to a wide array of systems failing under constant external strain and random perturbations. Past research focused on analytic and numerical…
We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers $\pm q_0$. Such polymers, known as polyampholytes, are compact when completely neutral and expanded when highly charged. Our…
We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
We construct forests that span $\mathbb{Z}^d$, $d\geq2$, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For $d\geq3$, two independent copies of…
We study the depinning transition of the $1+1$ dimensional directed polymer in a random environment with a defect line. The random environment consists of i.i.d. potential values assigned to each site of $\mathbb{Z}^2$; sites on the…
The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial…
Respiration measurements of whole tree plants have been reported that give evidence that the relative per volume/mass unit respiration decreases with increase of tree body size. In this study, based on the available data published a…