Related papers: Universal behaviour of 3D loop soup models
Many low temperature disordered systems are expected to exhibit Poisson-Dirichlet (PD) statistics. In this paper, we focus on the case when the underlying disorder is a logarithmically correlated Gaussian process $\phi_N$ on the box…
There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…
A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson's circular ensemble. We argue that the impact of localization in such systems is to provide…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
Random flights in $\mathbb{R}^d,d\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\underline{\bf X}_d(t),\,t>0,$ when the number of…
The domain-area distribution in the phase transition dynamics of ${\rm Z}_2$ symmetry breaking is studied theoretically and numerically for segregating binary Bose--Einstein condensates in quasi-two-dimensional systems. Due to the dynamic…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical…
At lower energies, the resonances in scattering experiments are often isolated. In quantum chaotic many-body, disordered or generically stochastic systems, the resonances overlap at larger energies. Eventually, the Ericson regime is reached…
When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order…
Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge…
Consider a sequence of Poisson point processes of non-trivial loops with certain intensity measures $(\mu^{(n)})_n$, where each $\mu^{(n)}$ is explicitly determined by transition probabilities $p^{(n)}$ of a random walk on a finite state…
We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective…
Avalanches in mean-field models can be mapped to memoryless branching processes defining a universality class. We present a reduced expression mapping a broad family of critical and subcriticial avalanches in mean-field models at the…
Within the framework of a (1+1)--dimensional model which mimics high energy QCD, we study the behavior of the cross sections for inclusive and diffractive deep inelastic $\gamma^*h$ scattering cross sections. We analyze the cases of both…
It is well known that the similar universal behavior of infinite-size (bulk) systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short- or long-range) of the…
We introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two--dimensional interacting particle systems, including Dyson Brownian motion, Nonintersecting Bernoulli/Poisson random walks, $\beta$--corners…
The distortion of the regular motion in a quantum system by its coupling to the continuum of decay channels is investigated. The regular motion is described by means of a Poissonian ensemble. We focus on the case of only few channels K<10.…
Most periodic systems are governed by short-range interactions as long-range interactions in these systems diminish uniformly. In this letter, however, we demonstrate that this is not true for a more general class of systems, which possess…
We consider two different systems exhibiting a continuous phase transition into an absorbing state. Both models belong to the same universality class, i.e., they are characterized by the same scaling functions and the same critical…