Related papers: Non-directed polymers in heavy-tail random environ…
In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with…
Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the…
For the quantum Ising model with ferromagnetic random couplings $J_{i,j}>0$ and random transverse fields $h_i>0$ at zero temperature in finite dimensions $d>1$, we consider the lowest-order contributions in perturbation theory in…
We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring…
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk.…
In this paper, we investigate a model for a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the…
We study the asymptotic properties of nearest-neighbor random walks in 1d random environment under the influence of an external field of intensity $\lambda\in\mathbb{R}$. For ergodic shift-invariant environments, we show that the limiting…
Let X= {X_t, t \ge 0} be a continuous time random walk in an environment of i.i.d. random conductances {\mu_e \in [1, \infty), e \in E_d}, where E_d is the set of nonoriented nearest neighbor bonds on the Euclidean lattice Z^d and d\ge 3.…
The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the…
Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space, and its…
We consider the random walk of a particle in a two-dimensional self-affine random potential of Hurst exponent $H=1/2$ in the presence of an external force $F$. We present numerical results on the statistics of first-passage times that…
Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers…
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…
In order to probe with high precision the tails of the ground-state energy distribution of disordered spin systems, K\"orner, Katzgraber and Hartmann \cite{Ko_Ka_Ha} have recently proposed an importance-sampling Monte-Carlo Markov chain in…
We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle $\theta$ to the surface. We use the canonical self-avoiding walk model of polymers and obtain the phase…
We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated…
We study the asymptotic distribution of random walks on $\mathbb Z^d$ ($d\ge1$) in deterministic reversible environments defined by an assignment of a positive conductance to each edge of $\mathbb Z^d$. We identify a deterministic set of…
We use an off - lattice bead - spring model of a self - avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte - Carlo (MC) simulation. The chain center of mass mean-squared…