Related papers: Internal DLA and the Gaussian free field
In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation ($DLA$) in which the radii of the particles are…
Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0, c l0, c^2 l0,... where c is a preferred scaling ratio and l0 a microscopic…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
Consider the parabolic Anderson model $\partial_tu=\frac{1}{2}\partial_x^2u+u\, \eta$ on the interval $[0, L]$ with Neumann, Dirichlet or periodic boundary conditions, driven by space-time white noise $\eta$. Using Malliavin-Stein method,…
We study analytically the correlations between the positions of tagged particles in the random average process, an interacting particle system in one dimension. We show that in the steady state the mean squared auto-fluctuation of a tracer…
We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved…
This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More…
We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear…
In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike…
We study the distribution of the maximum of a large class of Gaussian fields indexed by a box $V_N\subset Z^d$ and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that…
Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…
Very precise observational data are needed for studying the stellar cluster parameters (distance, reddening, age, metallicity) and cluster internal kinematics. In turn, these give us an insight into the properties of our Galaxy, for…
We consider the double-dimer model in the upper-half plane discretized by the square lattice with mesh size $\delta$. For each point $x$ in the upper half-plane, we consider the random variable $N_\delta(x)$ given by the number of the…
The mean intracluster gas fraction of X-ray clusters within their hydrostatic regions is derived from recent observational compilations of David, Jones & Forman and White & Fabian. At radii encompassing a mean density 500 times the critical…
Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by…
The properties of the galaxy distribution at large scales are usually studied using statistics which are assumed to be self-averaging inside a given sample. We present a new analysis able to quantitatively map galaxy large scale structures…
Let $X$ be a $d\times d$ symmetric random matrix with independent but non-identically distributed Gaussian entries. It has been conjectured by Lata\l{a} that the spectral norm of $X$ is always of the same order as the largest Euclidean norm…
We consider the equilibrium surface of the Random Average Process started from an inclined plane, as seen from the height of the origin, obtained in [Ferrari & Fontes, 1998], where its fluctuations were shown to be of order of the square…
We simulate 50 off-lattice DLA clusters, one million particles each. The probability distribution of the angle of attachment of arriving particles with respect to the local radial direction is obtained numerically. For increasing cluster…
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new…