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Standard geostatistical models assume stationarity and rely on a variogram model to account for the spatial dependence in the observed data. In some instances, this assumption that the spatial dependence structure is constant throughout the…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $\Delta \phi$ relative to the critical jammed state, the shear strain $\epsilon$,…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…
Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`{e}ve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of…
We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
The modeling of risk situations that occur in a space-time framework can be done using max-stable random fields on lattices. Although the summary coefficients for the spatial and temporal behaviour do not characterize the finite-dimensional…
A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent \theta =2/N, with N=1,2,3 ...…
Conditional auto-regressive (CAR) distributions are widely used to induce spatial dependence in the geographic analysis of areal data. These distributions establish multivariate dependence networks by defining conditional relationships…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
We derive a general expression for the large-scale halo bias, in theories with a scale-dependent linear growth, using the excursion set formalism. Such theories include modified gravity models, and models in which the dark energy clustering…
This paper covers the material of our two talks. We describe a series of projects based upon perturbative expansions to follow the gravitational evolution of the one point probability distribution functions (PDFs) for the density contrast…
We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest…
We present a study of the scaling properties of cluster-cluster aggregation with a source of monomers in the stationary state when the spatial transport of particles occurs by Levy flights. We show that the transition from mean-field…
We discuss existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated in the dynamic. To this end, we consider the convergence of the backward iterations of dependent…
Using the hierarchical approximation, we discuss the cut-off dependence of the renormalized quantities of a scalar field theory. The naturalness problem and questions related to triviality bounds are briefly discussed. We discuss unphysical…
We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d…
Motivated by the ubiquity of turbulent flows in realistic conditions, effects of turbulent advection on two models of classical non-linear systems are investigated. In particular, we analyze model A (according to the Hohenberg-Halperin…