Related papers: Kang-Redner Anomaly in Cluster-Cluster Aggregation
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…
For a class of aggregation models on the integer lattice $\mathbb{Z}^d$, $d\geq 2$, in which clusters are formed by particles arriving one after the other and sticking irreversibly where they first hit the cluster, including the classical…
Let $K$ and $K_0$ be convex bodies in $\mathbb{R}^d$, such that $K$ contains the origin, and define the process $(K_n, p_n)$, $n \geq 0$, as follows: let $p_{n+1}$ be a uniform random point in $K_n$, and set $K_{n+1} = K_n \cap (p_{n+1} +…
Particle pair (relative) diffusion in a field of homogeneous turbulence with generalised power-law energy spectra, $E(k)\sim k^{-p}$ for $1< p\le 3$ and $k_1\le k\le k_\eta$ with $k_\eta/k_1=10^6$, is investigated numerically using…
Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied with making use of the supersymmetric $\sigma$--model approach, in combination with the saddle--point method. The…
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the…
In the spirit of recent works on topological chaos generated by sequential rotation of infinitely thin stirrers placed in a viscous liquid, we consider the statistical properties of braiding exponent which quantitatively characterizes the…
We investigate the asymptotic behavior of the solutions to the Klein-Gordon and Dirac equations using the local spatial averaging approach to Bohr's correspondence principle in the large principal quantum number regime. The procedure is…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We consider a particle moving in $d\geq 2$ dimensions, its velocity being a reversible diffusion process, with identity diffusion coefficient, of which the invariant measure behaves, roughly, like $(1+|v|)^{-\beta}$ as $|v|\to \infty$, for…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
We consider the Random-Cluster model on $(\mathbb{Z}/n\mathbb{Z})^d$ with parameters $p \in (0,1)$ and $q\ge 1$. This is a generalization of the standard bond percolation (with open probability $p$) which is biased by a factor $q$ raised to…
The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy,…
Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the…
Exponential dispersion model is a useful framework in machine learning and statistics. Primarily, thanks to the additive structure of the model, it can be achieved without difficulty to estimate parameters including mean. However, tight…
This paper describes the Difference-of-Log-Normals (DLN) distribution. A companion paper makes the case that the DLN is a fundamental distribution in nature, and shows how a simple application of the CLT gives rise to the DLN in many…
We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
For a finite measure $\varLambda$ on $[0,1]$, the $\varLambda$-coalescent is a coalescent process such that, whenever there are $b$ clusters, each $k$-tuple of clusters merges into one at rate…
The density matrix renormalization group (DMRG) method allows an efficient computation of the properties of interacting 1D quantum systems. Two-dimensional (2D) systems, capable of displaying much richer quantum behavior, generally lie…