Related papers: On the statistical physics of directed polymers in…
We consider the complex polymer system, consisting of ring polymer connected to the $f_1$-branched star-like structure, in good solvent in presence of structural inhomogeneities. We assume, that structural defects are correlated at large…
In this paper, we investigate normal trees of directed graphs, which extend the fundamental concept of normal trees of undirected graphs. We prove that a directed graph $D$ has a normal spanning tree if and only if the topological space…
We prove a formula conjectured in O'Connell and Yor (2001) for the free energy density of a directed polymer in a Brownian environment in 1+1 dimensions.
We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in presence of disorder, equivalent to the KPZ equation on the half space with droplet initial conditions. From a Bethe Ansatz solution of the…
Let $d \geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is…
We present results about large deviations and laws of large numbers for various polymer related quantities. In a completely general setting and strictly positive temperature, we present results about large deviations for directed polymers…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
The tree code for the approximate evaluation of gravitational forces is extended and substantially accelerated by including mutual cell-cell interactions. These are computed by a Taylor series in Cartesian coordinates and in a completely…
We show that a randomly perturbed digraph, where we start with a dense digraph $D_\alpha$ and add a small number of random edges to it, will typically contain a fixed orientation of a bounded degree spanning tree. This answers a question…
We draw a certain analogy between the classical information-theoretic problem of lossy data compression (source coding) of memoryless information sources and the statistical mechanical behavior of a certain model of a chain of connected…
We consider directed random polymers in $(d+1)$ dimensions with nearly gamma i.i.d. disorder. We study the partition function $Z_{N,\omega}$ and establish exponential concentration of $\log Z_{N,\omega}$ about its mean on the subgaussian…
We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse…
Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method…
The joint statistical properties of two free energies computed at two different temperatures in {\it the same sample} of $(1+1)$ directed polymers is studied in terms of the replica technique. The scaling dependence of the reduced free…
A subset of leaves of a rooted tree induces a new tree in a natural way. The density of a tree $D$ inside a larger tree $T$ is the proportion of such leaf-induced subtrees in $T$ that are isomorphic to $D$ among all those with the same…
This is the first in a series of two works which study the discrete Gaussian free field on the binary tree when all leaves are conditioned to be positive. In this work, we obtain sharp asymptotics for the probability of this "hard-wall…
The last decade has witnessed a growing interest in random forest models which are recognized to exhibit good practical performance, especially in high-dimensional settings. On the theoretical side, however, their predictive power remains…
In this paper we study asymptotic properties of random forests within the framework of nonlinear time series modeling. While random forests have been successfully applied in various fields, the theoretical justification has not been…
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a particle has been grabbed then it cannot be…
Despite their remarkable effectiveness and broad application, the drivers of success underlying ensembles of trees are still not fully understood. In this paper, we highlight how interpreting tree ensembles as adaptive and self-regularizing…