Related papers: Random polymers on the complete graph
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
The asymptotic analytic expression for the two-time free energy distribution function in (1+1) random directed polymers is derived in the limit when the two times are close to each other
We determine the probability thresholds for the existence of monotone paths, of finite and infinite length, in random oriented graphs with vertex set $\mathbb N^{[k]}$, the set of all increasing $k$-tuples in $\mathbb N$. These graphs…
In this article, we try to give a rather complete picture of the behavior of the free energy for a model of directed polymer in a random environment, in which the polymer is a simple symmetric random walk on the lattice $\Z^d$, and the…
We establish some conditions under which $\text{GL}(d,\mathbb{R})$-valued cocycles over a subshift of finite type, equipped with an equilibrium state, exhibit exponential asymptotics for the spectral radius. Specifically, we show that the…
A model based on the aspect of the distribution of the length of conduction paths accessible for electric charge flow reproduces the universal power-law dispersive ac conductivity observed in polymer networks and, generally, in disordered…
We analyze conformational properties of branched polymer structures, formed on the base of Erd\"os-R\'enyi random graph model. We consider networks with $N=5$ vertices and variable parameter $c$, that controls graph connectedness. The…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by $H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx +…
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…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…
The one dimensional direct polymer in random media model is investigated using a variational approach in the replica space. We demonstrate numerically that the stable point is a maximum and the corresponding statistical properties for the…
We study an undirected polymer chain living on the 1-dimensional integer lattice and carrying i.i.d.\ random charges. Each self-intersection of the polymer contributes to the Hamiltonian an energy that is equal to the product of the charges…
We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we…
Given a class $\mathcal G$ of graphs, let ${\mathcal G}_n$ denote the set of graphs in $\mathcal G$ on vertex set $[n]$. For certain classes $\mathcal G$, we are interested in the asymptotic behaviour of a random graph $R_n$ sampled…
We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height…
In this paper we study the asymptotic behavior of the maximum magnitude of a complex random polynomial with i.i.d. uniformly distributed random roots on the unit circle. More specifically, let $\{n_k\}_{k=1}^{\infty}$ be an infinite…
Suppose that A_1,\dots, A_N are independent random matrices whose atoms are iid copies of a random variable \xi of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when \xi is gaussian then…
The a.s. existence of a polymer probability in the infinite volume limit is readily obtained under general conditions of weak disorder from standard theory on multiplicative cascades or branching random walk. However, speculations in the…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…