Related papers: Stochastic Growth in One Dimension and Gaussian Mu…
We introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
The one-dimensional polynuclear growth model with external sources at edges is studied. The height fluctuation at the origin is known to be given by either the Gaussian, the GUE Tracy-Widom distribution, or certain distributions called…
We show that the behavior of stochastic gradient descent is related to Bayesian statistics by showing that SGD is effectively diffusion on a fractal landscape, where the fractal dimension can be accounted for in a purely Bayesian way. By…
We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…
We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and…
We study the morphology of magnetic domain growth in disordered three dimensional magnets. The disordered magnetic material is described within the random-field Ising model with a Gaussian distribution of local fields with width $\Delta$.…
We study a stochastic Laplacian growth model, where a set $\mathbf{U}\subseteq\mathbb{R}^{\mathrm{d}}$ grows according to a reflecting Brownian motion in $\mathbf{U}$ stopped at level sets of its boundary local time. We derive a scaling…
We consider Evolution Strategies operating only with isotropic Gaussian mutations on positive quadratic objective functions, and investigate the covariance matrix when constructed out of selected individuals by truncation. We prove that the…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation arising to characterize the limit spectral measure of the…
Primordial non-Gaussianity (PNG) is a signature of fundamental physics in the early universe that is probed by cosmological observations. It is well known that the local type of PNG generates a strong signal in the two-point function of…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…