相关论文: Estimates on path delocalization for copolymers at…
In this paper, we study a model of directed polymers in random environment, where the environment is restricted to a time-space tube whose spatial width grows polynomially with time. It can be viewed as an interpolation between the…
We consider the optimal paths in a $d$-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential.…
According to recent progress in the finite size scaling theory of critical disordered systems, the nature of the phase transition is reflected in the distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$…
We investigate theoretically the transfer of excitation along a one dimensional chain of monomers for a situation in which initially the excitation is shared coherently by two monomers. We show that depending on the relative phase between…
We consider the point-to-point half-space log-gamma polymer model in the unbound phase. We prove that the free energy increment process on the anti-diagonal path converges to the top marginal of a two-layer Markov chain with an explicit…
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 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…
Polymers confined in corrugated channels, i.e. channels of varying amplitude, display {multiple local maxima and minima of the diffusion coefficient upon increasing their degree of polymerization $N$}. We propose a theoretical effective…
In this paper, we study the localization length of the $1+1$ continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the quenched polymer measure. We show that the localization…
We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel…
We consider a directed polymer interacting with a diluted pinning potential restricted to a line. We characterize explicitely the set of disorder configurations that give rise to localization of the polymer. We study both relevant cases of…
We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in…
It is a well-known open problem in the literature on random polymers to show that a directed polymer in random environment localizes around a favorite path at low temperature. A precise statement of this conjecture is formulated and proved…
We study the depinning transition of the $1+1$ dimensional directed polymer in a random environment with a defect line. The random environment consists of i.i.d. potential values assigned to each site of $\mathbb{Z}^2$; sites on the…
We consider a diffuse interface model describing a ternary system constituted by a conductive diblock copolymer and a homopolymer acting as solvent. The resulting dynamics is modeled by two Cahn--Hilliard--Oono equations for the copolymer…
We consider a generalization of the classical pinning problem for integer-valued random walks conditioned to stay non-negative. More specifically, we take pinning potentials of the form $\sum_{j\geq 0}\epsilon_j N_j$, where $N_j$ is the…
We investigate the delocalization and conductance quantization in finite one-dimensional chains with only off-diagonal disorder coupled to leads. It is shown that the appearence of delocalized states at the middle of the band under…
We consider a model for a polymer chain interacting with a sequence of equispaced flat interfaces through a pinning potential. The intensity $\delta \in \mathbb {R}$ of the pinning interaction is constant, while the interface spacing…
We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the…
We calculate the two, three, four, and five-body (state independent) effective potentials between the centers of mass (CM) of self avoiding walk polymers by Monte-Carlo simulations. For full overlap, these coarse-grained n-body interactions…