Related papers: Scaling transition for long-range dependent Gaussi…
A natural generalization of the CSL (Continuous Spontaneous Localization) theory of dynamical collapse is applied to a relativistic quantum scalar field $\phi({\bf x},t)$. It is shown that the modified Schr\"odinger equation is…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
We investigate scaling phenomena at first-order quantum transitions, when the boundary conditions favor one of the two phases. We show that the corresponding finite-size scaling behavior, arising from the interplay between the driving…
We have measured the temperature dependence of the longitudinal resistivity $% \rho_{xx}$ of a two-dimensional electron system in the regime of the quantum Hall plateau transition. We extracted the quantitative form of scaling function for…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
In this paper, for centered homogeneous Gaussian random fields the joint limiting distributions of normalized maxima and minima over continuous time and uniform grids are investigated. It is shown that maxima and minima are asymptotic…
We consider Gaussian subordinated L\'evy fields (GSLFs) that arise by subordinating L\'evy processes with positive transformations of Gaussian random fields on some spatial domain $\mathcal{D}\subset \mathbb{R}^d$, $d\geq 1$. The resulting…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and…
For any given algebra of local observables in relativistic quantum field theory there exists an associated scaling algebra which permits one to introduce renormalization group transformations and to construct the scaling (short distance)…
We extend previous results due to Ding and Zhuang in order to prove that a phase transition occurs for the long range Ising model in lower dimensions. By making use of a recent argument due to Affonso, Bissacot and Maia from 2022 which…
We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. We focus fir st on consistent polygonal fields, for which we show Markovianity and…
We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. We define and study candidates for such limits in…
We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaussian process with independent coefficients when expanded in…
We present exact formulas for both the expected number and the height distribution of local maxima (peaks) in two distinct categories of smooth, non-centered Gaussian fields: (i) nonstationary Gaussian processes and (ii) stationary planar…
By extending the quantum evolution of a scalar field in time-dependent backgrounds to the complex-time plane and transporting the in-vacuum along a closed path, we argue that the geometric transition from the simple pole at infinity…
This note is about a drift-diffusion process $X$ with a time-independent, divergence-free drift $b$, where $b$ is a smooth Gaussian field that decorrelates over large scales. In two space dimensions, this just fails to fall into the…