Related papers: Internal DLA and the Gaussian free field
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
We consider a high-dimensional mixture of two Gaussians in the noisy regime where even an oracle knowing the centers of the clusters misclassifies a small but finite fraction of the points. We provide a rigorous analysis of the…
We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance $r$ from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the…
This paper consists of two parts. In the first part, we focus on the average of a functional over shifted Gaussian homogeneous noise and as the averaging domain covers the whole space, we establish a Breuer-Major type Gaussian fluctuation…
We consider "nonconventional" averaging setup in the form $\frac {dX^\epsilon(t)}{dt}=\epsilon B\big(X^\epsilon(t),\xi(q_1(t)), \xi(q_2(t)),...,\xi(q_\ell(t))\big)$ where $\xi(t),t\geq 0$ is either a stochastic process or a dynamical system…
We discuss how the statistical properties of the area and radius of gyration of single self-avoiding loops, and of Ising and percolation cluster boundaries, may be calculated using ideas of two-dimensional field theory. For cluster…
We examine the nature of galaxy clustering in redshift space using a method based on an expansion of the galaxian density field in Spherical Harmonics and linear theory. We derive a compact and self-consistent expression for the distortion…
We investigate the percolation phase transition for level sets of the Gaussian free field on $\mathbb{Z}^d$, with $d\geqslant 3$, and prove that the corresponding critical parameter $h_*(d)$ is strictly positive for all $d\geqslant3$, thus…
Two sets of objects of size $n$ are to be matched to each other based on i.i.d. costs associated to every pair of objects. Objects prefer to be matched as cheaply as possible, and a matching is said to be stable if there is no pair of…
Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…
A scaling theory is used to derive the dependence of the average number <k> of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions…
In this note, we prove Gaussian field convergence of fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet.
We present a systematic formulation of the performance of a ring laser gyro (RLG) under the influence of a randomized sinusoidal dither. We develop the Fokker Planck equation of such a system and find its steady state solution that we use…
We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from…
We consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the tail $n^{(d-2)/4}(W_\infty - W_n)$ of the normalized partition function. It was proven by Comets and Liu, that for sufficiently…
We estimate the probability that the discrete Gaussian free field on a planar domain with Dirichlet boundary conditions stays positive in the bulk. Improving upon the result by Bolthausen, Deuschel and Giacomin from 2001, we derive the…
We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly…
Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However,…
(Abridged) By comparing the frequency of typical events with that of unusual events, one can test whether the cosmological density distribution function is consistent with the normally made assumption of Gaussianity. To this end, we compare…
Random advection of Lagrangian tracer scalar field $\theta (t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral…