Related papers: On high dimensional directed polymer in random med…
For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…
We propose exploiting symmetries (exact or approximate) of the Standard Model (SM) to search for physics Beyond the Standard Model (BSM) using the data-directed paradigm (DDP). Symmetries are very powerful because they provide two samples…
In the present work, we investigate the case of Directed Polymer in a Random Environment (DPRE), when the increments of the random walk are heavy-tailed with tail-exponent equal to zero ($\mathbf{P}[|X_1|\geq n]$ decays slower than any…
The aim of this paper is to investigate the distribution of a continuous homopolymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously vary two parameters: the…
Directed polymers (strings) and semiflexible polymers (filaments) are one-dimensional objects governed by tension and bending energy, respectively. They undergo unbinding transitions in the presence of a short-range attractive potential.…
It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation…
We study the Directed Polymer model subject to a particular form of disorder, $\eta(x,t)=\eta_X(x) \eta_T(t)$, recently proposed in biological applications. We find that two new universality classes arise, depending on the the lattice…
The drag of turbulent flows can be drastically decreased by addition of small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the…
We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with…
We realized one dimensional disordered photonic structures by grouping high refractive index layers in clusters, randomly distributed in such structure. We have control on the maximum size of the cluster and on the ratio high-low refractive…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several…
The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in…
Hybrid molecular dynamics/Monte Carlo simulations used to study melts of unentangled, thermoreversibly associating supramolecular polymers. In this first of a series of papers, we describe and validate a model that is effective in…
This study uses the link between extreme value laws and dynamical systems theory to show that important dynamical quantities as the correlation dimension, the entropy and the Lyapunov exponents can be obtained by fitting observables…
For a Brownian directed polymer in a Gaussian random environment, with $q(t,\cdot)$ denoting the quenched endpoint density and \[ Q_n(t,x_1,\ldots,x_n)=\mathbf{E}[q(t,x_1)\ldots q(t,x_n)], \] we derive a hierarchical PDE system satisfied by…
We investigate one dimensional tight binding model in the presence of a correlated binary disorder. The disorder is due to the interaction of particles with heavy immobile other species. Off-diagonal disorder is created by means of a fast…
In this paper, we study random walks evolving with a directional bias in a two-dimensional random environment with correlations that vanish polynomially. Using renormalization methods first employed for one-dimensional dynamic environments…