Related papers: The high-temperature behavior for the directed pol…
In this paper, we study the free energy of the directed polymer on a cylinder of radius $L$ with the inverse temperature $\beta$. Assuming the random environment is given by a Gaussian process that is white in time and smooth in space, with…
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…
The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $\beta\to 0$ under the assumption that random environment satisfies a certain…
The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length $L$, the high temperature phase is characterized by a diffusive behavior for the end-point displacement…
We consider the behavior of the quantity $p(\beta)$; the free energy of directed polymers in random environment in $1+2$ dimension, where $\beta$ is inverse temperature. We know that the free energy is strictly negative when $\beta$ is not…
We introduce a new disorder regime for directed polymers with one space and one time dimension that is accessed by scaling the inverse temperature parameter \beta with the length of the polymer n. We scale \beta_n := \beta n^{-\alpha} for…
We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…
Following a recent work by Yoshino, we study the aging dynamics of a directed polymer in random media, in 1+1 dimensions. Through temperature quench, and temperature cycling numerical experiments similar to the experiments on real spin…
In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which allows to compute the scaling exponent $\theta$ of the free energy…
We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at…
The joint statistical properties of two free energies computed at two different temperatures in {\it the same sample} of $(1+1)$ directed polymers is studied in terms of the replica technique. The scaling dependence of the reduced free…
We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse…
We present systematic numerical simulations for directed polymers at finite temperatures in 1+1 and 2+1 dimensions. The transverse fluctuations and free energy fluctuations tend to the strong coupling limit at any temperature in both 1+1…
We study the Cauchy directed polymer model on $\mathbb{Z}^{1+1}$, where the underlying random walk is in the domain of attraction to the $1$-stable law. We show that, if the random walk satisfies certain regularity assumptions and its…
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 introduce a new disorder regime for directed polymers in dimension $1+1$ that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter…
The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel~\cite{AKQ12}. It was proved that at inverse temperature $\beta n^{-\gamma}$ with $\gamma=1/4$ the partition function, centered…
In dimensions 3 or larger, it is a classical fact that the directed polymer model has two phases: Brownian behavior at high temperature, and non-Brownian behavior at low temperature. We consider the response of the polymer to an external…
Directed polymers on 1+1 dimensional lattices coupled to a heat bath at temperature $T$ are studied numerically for three ensembles of the site disorder. In particular correlations of the disorder as well as fractal patterning are…
We consider a directed polymer of length $N$ interacting with a linear interface. The monomers carry i.i.d. random charges $(\omega_i)_{i=1}^N$ taking values in $\mathbb{R}$ with mean zero and variance one. Each monomer $i$ contributes an…