Related papers: Stationary DLA is well defined

Results from a modified Diffusion Limited Aggregation (DLA) model are presented. The modifications of the classical DLA model are in the attachment to the cluster rules and in the scheme of particle generation/killing. In the classical DLA…

Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…

The growth rate of the partial maximum of a stationary stable process was first studied in the works of Samorodnitsky (2004a,b), where it was established, based on the seminal works of Rosi\'nski (1995,2000), that the growth rate is…

We study the sizes of delta-additive sets of unit vectors in a d-dimensional normed space: the sum of any two vectors has norm at most delta. One-additive sets originate in finding upper bounds of vertex degrees of Steiner Minimum Trees in…

I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the…

In the development of a presumed asymptotic expansion for lambda_d in previous work, a basic step involved extracting the asymptotic behavior of a sum as being dominated by the largest term in the sum. But this argument only is valid when…

We study variational models for dislocations in three dimensions in the line-tension scaling. We present a unified approach which allows to treat energies with subquadratic growth at infinity and other regularizations of the singularity…

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via \Gamma-convergence for rate-independent processes that energetic solutions of the quasi-static…

We prove mean and pointwise ergodic theorems for the action of a discrete lattice subgroup in a connected algebraic Lie group, on infinite volume homogeneous algebraic varieties. Under suitable necessary conditions, our results are…

We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization, characterized as an…

We consider hamiltonian systems with spatially varying effective mass and slowly varying local potential in d dimensions. The Slater sum is defined as the diagonal element of the Bloch propagator. We derive a gradient expansion of the…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

We consider the DLA process on a cylinder G x N. It is shown that this process "grows arms", provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the time it takes…

In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which…

We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior…

We consider an analogous version of the diffusion-limited aggregation model defined on the hyperbolic plane. We prove that almost surely the aggregate viewed at time infinity will have a positive density.

This paper is about the homogenization of linear elliptic operators in divergence form with stationary random coefficients that have only slowly decaying correlations. It deduces optimal estimates of the homogenization error from optimal…

We consider the lattice dynamics in the harmonic approximation for We consider the lattice dynamics in the harmonic approximation for a simple hypercubic lattice with arbitrary unit cell. The initial data are random according to a…

We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is an LQG harmonic ball, which we constructed in a…

Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…