Related papers: A simple fluctuation lower bound for a disordered …
We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents…
We consider simple random walk on a discrete cylinder with base a large d-dimensional torus of side-length N, when d is two or more. We develop a stochastic domination control on the local picture left by the random walk in boxes of…
In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with…
Consider the centered Gaussian field on the lattice $\mathbb{Z}^d,$ $d$ large enough, with covariances given by the inverse of $\sum_{j=k}^K q_j(-\Delta)^j,$ where $\Delta$ is the discrete Laplacian and $q_j \in \mathbb{R},k\leq j\leq K,$…
At the mean-field level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of "structural glasses", with a "random first-order transition" (RFOT) characterized by a discontinuous…
We prove, for any $\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at…
When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin…
We address the problem of infrared singularities in the perturbation theory for disordered interacting systems in $d\leq 2$. We show that a typical, sufficiently large interacting system exhibits a linear instability in the spin triplet…
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…
We study conductance fluctuations in random resistor networks with hyperuniform bond disorder, where the fluctuations of the number of bonds present in a test volume $V$ scale as $V^{-a}$ with $a > 1/2$. Since small changes in the…
We study the fluctuations of random surfaces on a two-dimensional discrete torus. The random surfaces we consider are defined via a nearest-neighbor pair potential which we require to be twice continuously differentiable on a (possibly…
The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the…
We study, using functional renormalization (FRG), two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depend on a non trivial boundary layer regime with (possibly multiple) chaos…
Spin chains with symmetry-protected edge zero modes can be seen as prototypical systems for exploring topological signatures in quantum systems. These are useful for robustly encoding quantum information. However in an experimental…
We study the delocalization by bulk randomness of a single flux line (FL) from an extended defect, such as a columnar pin or twin plane. In three dimensions, the FL is always bound to a planar defect, while there is an unpinning transition…
In this letter, we fill a hole in the existing literature about disordered quantum spin systems generated by a random local interaction $\{\mathfrak{h}(Z)\}_{Z\Subset \mathbb{Z}^\nu}$ satisfying a statistical version of translation…
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…
Using an ensemble of high resolution 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual $N$--point volume-averaged…
We study the spin transport properties of some disordered spin chains with a special focus on the distribution of the frequency-dependent spin conductivity. In the cases of interest here, the systems are governed by an effectively infinite…
We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one--dimensional integer lattice and grows in discrete time: (1) the height above the site $x$…