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We investigate the time averaged squared displacement (TASD) of continuous time random walks with respect to the number of steps $N$, which the random walker performed during the data acquisition time $T$. We prove that the TASD, and as…
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…
We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
We investigate, using numerical simulations and analytical arguments, a simple one dimensional model for the swelling or the collapse of a closed polymer chain of size N, representing the dynamical evolution of a polymer in a \Theta-solvent…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
We propose a new formulation of the probability distribution function of wind driven water surface slope with an $\alpha$-stable distribution probability. The mathematical formulation of the probability distribution function is given under…
As solute molecules permeate into a vesicle due to a concentration difference across its membrane, the vesicle swells through osmosis. The swelling can be divided into two stages: (a) an "ironing" stage, where the volume-to-area ratio of…
We generalize Huberman-Rudnick universal scaling law for all periodic windows of the logistic map and show the robustness of $q$-Gaussian probability distributions in the vicinity of chaos threshold. Our scaling relation is universal for…
The number of free sites next to the end of a self-avoiding walk is known as the atmosphere. The average atmosphere can be related to the number of configurations. Here we study the distribution of atmospheres as a function of length and…
We study self-avoiding walks on the four-dimensional hypercubic lattice via Monte Carlo simulations of walks with up to one billion steps. We study the expected logarithmic corrections to scaling, and find convincing evidence in support the…
Wavefunction collapse models modify Schr\"odinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum…
The Pairwise Einstein Model (PEM) of steps not only justifies the use of the Generalized Wigner Distribution (GWD) for Terrace Width Distributions (TWDs), it also predicts a specific form for the Step Position Distribution (SPD), i.e., the…
In this paper, we study the overlap distribution and Gibbs measure of the Branching Random Walk with Gaussian increments on a binary tree. We first prove that the Branching Random Walk is 1 step Replica Symmetry Breaking and give a precise…
We have simulated four-dimensional interacting self-avoiding trails (ISAT) on the hyper-cubic lattice with standard interactions at a wide range of temperatures up to length 4096 and at some temperatures up to length 16384. The results…
A two-dimensional array of independent random signs produces coalescing random walks. The position of the walk, starting at the origin, after N steps is a highly nonlinear, noise sensitive function of the signs. A typical term of its…
Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered…