Related papers: Directed polymers on infinite graphs
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
We prove a distributional limit theorem conjectured in [Journal of Statistical Physics 174, No. 6, 1372-1403 (2019)] for partition functions defining models of directed polymers on diamond hierarchical graphs with disorder variables placed…
We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with…
I discuss models for a continuum directed random polymer in a disordered environment in which the polymer lives on a fractal called the \textit{diamond hierarchical lattice}, a self-similar metric space forming a network of interweaving…
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…
We provide a new short and elementary proof of diffusivity for directed polymer in a random environment in the weak disorder phase.
In this work we are concerned with the crossover between strong disorder (SD) and weak disorder (WD) behaviors in three well-known problems that involve minimal paths: directed polymers (directed paths with fixed starting point and length),…
We associate root polytopes to directed graphs and study them by using ribbon structures. Most attention is paid to what we call the semi-balanced case, i.e., when each cycle has the same number of edges pointing in the two directions.…
We show that the weak disorder phase for the directed polymer model in a bounded random environment is characterized by the integrability of the running supremum $\sup_{n\in \mathbb N}W_n^\beta$ of the associated martingale…
The distribution of monomers along a linear polymer grafted on a hard wall is modelled by determining the probability distribution of occupied vertices of Dyck and ballot path models of adsorbing linear polymers. For example, the…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
For a directed polymer model in random environment, a characterization of the weak disorder phase in terms of the moment of the renormalized partition function has been proved in [S. Junk: Communications in Mathematical Physics 389,…
The phase diagram of the collapse of a two-dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the $q\to 1$ limit of an extension of the $q-$ states Potts model.…
We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed trough the random branching process.…
We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along…
We prove universality of Tracy-Widom GUE fluctuations for directed polymers in $1+1$ dimensions in the intermediate disorder regime. Building on the Lindeberg replacement method of arXiv:2304.04871, we refine estimates for the measure of…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…