Related papers: Directed polymers on infinite graphs
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
We introduce and study the planted directed polymer, in which the path of a random walker is inferred from noisy 'images' accumulated at each timestep. Formulated as a nonlinear problem of Bayesian inference for a hidden Markov model, this…
In this paper, we consider directed polymers in random environment with long range jumps in discrete space and time. We extend to this case some techniques, results and classifications known in the usual short range case. However, some…
We show that choosing appropriate distributions of the randomness, the search for optimal paths links diverse problems of disordered media like directed percolation, invasion percolation, directed and non-directed spanning polymers. We also…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
We study the long-range directed polymer model on $\mathbbm{Z}$ in a random environment, where the underlying random walk lies in the domain of attraction of an $\alpha$-stable process for some $\alpha\in(0,2]$. Similar to the more classic…
We study the Directed Polymer model subject to a particular form of disorder, $\eta(x,t)=\eta_X(x) \eta_T(t)$, recently proposed in biological applications. We find that two new universality classes arise, depending on the the lattice…
We consider a model of directed polymers on regular trees with complex-valued random weights introduced by Cook and Derrida [CD90] and studied mathematically by Derrida, Evans and Speer [DES93]. In addition to the usual weak-disorder and…
In the present work, we investigate the case of Directed Polymer in a Random Environment (DPRE), when the increments of the random walk are heavy-tailed with tail-exponent equal to zero ($\mathbf{P}[|X_1|\geq n]$ decays slower than any…
A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of $d\times d$ inverse-Wishart random matrices, so that the model nicely generalizes the well-studied log-gamma…
In this paper, we study the so-called intermediate disorder regime for a directed polymer in a random environment with heavy-tail. Consider a simple symmetric random walk $(S_n)_{n\geq 0}$ on $\mathbb{Z}^d$, with $d\geq 1$, and modify its…
In this article we study a \emph{non-directed} polymer model in dimension $d\ge 2$: we consider a simple symmetric random walk on $\mathbb{Z}^d$ which interacts with a random environment, represented by i.i.d. random variables…
Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the…
We show that the endpoint large deviation rate function for a continuous-time directed polymer agrees with the rate function of the underlying random walk near the origin in the whole weak disorder phase.
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
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…
Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed…
Directed polymers in random environment have usually been constructed with a simple random walk on the integer lattice. It has been observed before that several standard results for this model continue to hold for a more general reference…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
We study the directed polymer model in a bounded environment with bond disorder and show that, in the interior of the weak disorder phase, weak disorder continues to hold upon perturbation by a small bias. Using this stability result, we…