Related papers: Very Strong Disorder for the Parabolic Anderson mo…
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…
In this note we show that in any dimension $d$, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymers in a random environment : the parabolic Anderson…
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1+d)-dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d.…
We study a polymer model on hierarchical lattices very close to the one introduced and studied in \cite{DGr, CD}. For this model, we prove the existence of free energy and derive the necessary and sufficient condition for which very strong…
We investigate large deviations of the free energy in the O'Connell-Yor polymer through a variational representation of the positive real moment Lyapunov exponents of the associated parabolic Anderson model. Our methods yield an exact…
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 behavior of the elastic polymer, a model of a directed polymer in a continuous Gaussian random environment that is independent in time and correlated in space, as the dimension of the environment is taken to infinity. We give…
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 real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small…
We prove an invariance principle for the two-dimensional lattice parabolic Anderson model with small potential. As applications we deduce a Donsker type convergence result for a discrete random polymer measure, as well as a universality…
The spherical limit of strongly commensurate dirty-bosons is studied perturbatively at weak disorder and numerically at strong disorder in two dimensions (2D). We argue that disorder is not perfectly screened by interactions, and…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
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…
In this paper, we study a model of a Brownian polymer in $\mathbb {R}_+\times \mathbb {R}^d$, introduced by Rovira and Tindel [J. Funct. Anal. 222 (2005) 178--201]. Our investigation focuses mainly on the effect of strong spatial…
We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost…
We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the…
We give sharp estimate for the free energy of directed polymers in random environment in dimension 1+1. This estimate was known for a Gaussian environment, we extend it to the case where the law of the environment is infinitely divisible.
We study the global existence of the singular nonlinear parabolic Anderson model equation on $2$-dimensional tours $\mathbb{T}^2$. The method is based on paracontrolled distribution and renormalization. After split the original nonlinear…
Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for…
We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an…