Related papers: Crossing random walks and stretched polymers at we…
We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on Z^d with jump rate rho (that plays the role of the random medium), we modify the law of a…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
We consider a random walk on the support of a stationary simple point process on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the…
We consider random walks in random environments on Z^d. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments,…
We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with recent experiments of \emph{Escherichia coli}, the polymer dynamics are…
We study a model of continuous-time nearest-neighbor random walk on $\mathbb{Z}^d$ penalized by its occupation time at the origin, also known as a homopolymer. For a fixed real parameter $\beta$ and time $t>0$, we consider the probability…
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…
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 relationship between anomalous superdiffusive behavior and particle trapping probability is analyzed on a rocking ratchet potential with spatially correlated weak disorder. The trapping probability density is shown, analytically and…
We study the range of a planar random walk on a randomly oriented lattice, already known to be transient. We prove that the expectation of the range grows linearly, in both the quenched (for a.e. orientation) and annealed ("averaged")…
We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed…
In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges. There are two phases, localized and delocalized, depending on the inverse temperature and on the disorder bias. Using…
We investigate a model of chaperone-assisted polymer translocation through a nanopore in a membrane. Translocation is driven by irreversible random sequential absorption of chaperone proteins that bind to the polymer on one side of the…
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…
A model for studying the ultrametricity of the energy landscape in a disordered heteropolymer is presented. It is treated as a simplified model of a protein molecule in which amino acid residues are modeled as point masses. Pairwise…
Consider the invariance principle for a random walk with random environment (denoted by $\mu$) in time on $\bfR$ in a weak quenched sense. We show that a sequence of the random probability measures on $\bfR$ generated by a bounded Lipschitz…
We study a simple model for the trajectory of a particle in a turbulent fluid, where a Brownian motion travels through a random Gaussian velocity field. We study the quenched law of the process and prove that in a weak environment setting,…
Polymer chains with hard-core interaction on a two-dimensional lattice are modeled by directed random walks. Two models, one with intersecting walks (IW) and another with non-intersecting walks (NIW) are presented, solved and compared. The…
We consider a directed polymer model in dimension $1+1$, where the disorder is given by the occupation field of a Poisson system of independent random walks on $\mathbb Z$. In a suitable continuum and weak disorder limit, we show that the…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…