Related papers: Local scaling limits of L\'evy driven fractional r…
In this paper we study the local times of vector-valued Gaussian fields that are `diagonally operator-self-similar' and whose increments are stationary. Denoting the local time of such a Gaussian field around the spatial origin and over the…
In bootstrap percolation it is known that the critical percolation threshold tends to converge slowly to zero with increasing system size, or, inversely, the critical size diverges fast when the percolation probability goes to zero. To…
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic…
Multistable L\'evy motions are extensions of L\'evy motions where the stability index is allowed to vary in time. Several constructions of these processes have been introduced recently, based on Poisson and Ferguson-Klass-LePage series…
The field theoretic renormalization group and operator product expansion are applied to the problem of a passive scalar advected by the Gaussian nonsolenoidal velocity field with finite correlation time, in the presence of large-scale…
A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $\xi \sim \exp\left(A…
The impact of local space anisotropy on the transverse Doppler effect is examined. Two types of laboratory experiments aimed at seeking and measuring the local space anisotropy are proposed. In terms of the conventional special relativity…
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the…
The scaling function of the 2D Ising model in a magnetic field on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer matrix approach. The use of the Aharony-Fisher non-linear scaling…
Consider a random process s solution of the stochastic partial differential equation Ls = w with L a homogeneous operator and w a multidimensional L\'evy white noise. In this paper, we study the asymptotic effect of zooming in or zooming…
We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive-definite estimators, the sampling error at each site can be rigorously…
How many canonical degrees of freedom does a quantum field theory actually use during its Hamiltonian evolution? For a UV/IR-regularised classical scalar field, we address this question directly at the level of phase-space dynamics by…
We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of…
A fundamental relation in Lagrangian Kolmogorov theory is concerned with inertial range scaling of the second-order velocity structure function over intermediate time lags at sufficiently high Reynolds numbers. Significant theoretical…
In the paper we present simple examples of linear random fields defined on $\ZZ^2$ and $\ZZ^3$ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand…
We study a class of nonlocal conformal field theories in two dimensions which are obtained as deformations of the Virasoro minimal models. The construction proceeds by coupling a relevant primary operator $\phi_{r,s}$ of the $m$-th minimal…
An introduction into the theory of locally anisotropic spaces (modelled as vector bundles provided with compatible nonlinear and distinguished linear connections and metric structures and containing as particular cases different types of…
The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is solution to a stochastic differential equation driven by an…