Related papers: The Continuum Directed Random Polymer
We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer…
The explicit expression for the the probability distribution function of the endpoint fluctuations of one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated…
Inspired by applications, we consider reaction-diffusion equations on $\mathbb{R}$ that are stochastically forced by a small multiplicative noise term that is white in time, coloured in space and invariant under translations. We show how…
We study a Brownian particle passively driven by a field obeying the noisy Burgers equation. We demonstrate that the system exhibits replica symmetry breaking in the path ensemble with the initial position of the particle being fixed. The…
A variational method that allows for replica-symmetry breaking is applied to directed polymers in an (N+1)-dimensional disordered medium. The noise studied here has gaussian correlations, i.e. it is short-ranged. In dimensions N<2, the…
We study transport of an inertial Brownian particle moving in a symmetric and periodic one-dimensional potential, and subjected to both a symmetric, unbiased external harmonic force as well as biased dichotomic noise $\eta(t)$ also known as…
We investigate the dynamics of Brownian particles in internal state- dependent symmetric and periodic potentials. Although no space or time symmetry of the Hamiltonian is broken, we show that directed transport can appear. We demonstrate…
We consider the Brownian directed polymer in Poissonian environment in dimension 1+1, under the so-called intermediate disorder regime, which is a crossover regime between the strong and weak disorder regions. We show that, under a…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
The discrete polymer model with random Boltzmann weights with homogeneous inverse gamma distribution, introduced by Sepp\"al\"ainen, is studied in the case of a polymer with one fixed and one free end. The model with two fixed ends has been…
The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified…
This paper is a follow-up work of arxiv.org/abs/2101.05949. We study a non-directed polymer model in random environments. The polymer is represented by a simple symmetric random walk $S$ on $\mathbb{Z}^d$ with $d\geq2$ and the random…
We investigate the high-temperature behavior of the directed polymer model in dimension $1+2$. More precisely we study the difference $\Delta \mathtt{F}(\beta)$ between the quenched and annealed free energies for small values of the inverse…
We derive stationary measures for certain zero-temperature random polymer models, which we believe are new in the case of the zero-temperature limit of the beta random polymer (that has been called the river delta model). To do this, we…
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…
A polymer-chain network is a collection of interconnected polymer-chains, made themselves of the repetition of a single pattern called a monomer. Our first main result establishes that, for a class of models for polymer-chain networks, the…
We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicative white noise based on a fractal measure. We prove pathwise uniqueness for solutions of this equation when the noise coefficient is…
We consider a Hamiltonian involving the range of the simple random walk and the Wiener sausage so that the walk tends to stretch itself. This Hamiltonian can be easily extended to the multidimensional cases, since the Wiener sausage is…
We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative space-time white noise noise smoothed in space. For $d\geq 3$ and small noise intensity, the solution is known to converge to a strictly positive random variable…
Zero temperature limit in (1+1) directed polymers with finite range correlated random potential is studied. In terms of the standard replica technique it is demonstrated that in this limit the considered system reveals the one-step replica…