Related papers: Spatial random permutations and infinite cycles
Random point configurations are said to be in hyperuniform states, if density fluctuations are anomalously suppressed in large-scale. Typical examples are found in Coulomb gas systems in two dimensions especially called log-gases in random…
In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…
The quasi-static solutions of the matter density perturbation in various dark energy models and modified gravity models have been investigated in numerous papers. However, the oscillating solutions in those models have not been investigated…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
The recent suggestion that late time quantum dynamics may be important for resolving cosmological issues associated with our observed universe requires a consideration of several subtle issues associated with quantum cosmology, as we…
We consider a one-dimensional system of particles, moving at constant velocities chosen independently according to a symmetric distribution on $\{-1,0,+1\}$, and annihilating upon collision -- with, in case of triple collision, a uniformly…
We consider the quantum evolution of a fermion-hole pair in a d-dimensional gas of non-interacting fermions in the presence of random phase scattering. This system is mapped onto an effective Ising model, which enables us to show rigorously…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
A trapped Bose-Einstein condensate, being strongly perturbed, exhibits several spatial structures. First, there appear quantum vortices. Increasing the amount of the injected energy leads to the formation of vortex tangles representing…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one…
We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
The dynamics of an inhomogeneous universe is studied with the methods of Loop Quantum Cosmology as an example of the quantization of vacuum cosmological spacetimes containing gravitational waves (Gowdy spacetimes). The analysis performed at…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
We numerically study the momentum distribution of one-dimensional Bose and Fermi systems with long-range interaction $g/r^2$ for the ``special'' values $g= -\frac{1}{2}, 0, 4$, singled out by random matrix theory. The critical exponents are…
We discuss the relation between the "compositeness" of an s-wave bound state, as derived from a related partial wave scattering amplitude, and the corresponding spatial probability densities, for the case of spherically symmetric,…