Related papers: Spatial random permutations and infinite cycles
Quantum critical matter has already been studied in many systems, including cold atomic gases. We report the observation of a universal behaviour of ultracold quantum critical Bose gases in a one-dimensional optical lattice. In the quantum…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
We calculate certain features of Bose-Einstein condensation in the ideal gas by using recurrence relations for the partition function. The grand canonical ensemble gives inaccurate results for certain properties of the condensate that are…
We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…
We study classical continuous systems with singular distributions of velocities. Radon measures with the infinite mass give these distributions. Positions of particles in such systems are no longer usual configurations in the location…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic…
We propose a cosmological model in which the universe undergoes an endless sequence of cosmic epochs each beginning with a `bang' and ending in a `crunch.' The temperature and density are finite at each transition from crunch to bang.…
The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…
We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time…
We investigate an ultracold and dilute Bose gas by taking into account a finite-range two-body interaction. The coupling constants of the resulting Lagrangian density are related to measurable scattering parameters by following the…
Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…
A class of k-particle observables in a two-mode system of Bose particles is characterized by typicality: if the state of the system is sampled out of a suitable ensemble, an experimental measurement of that observable yields (almost) always…
The role of background in bosonic quantum statistics is discussed in the frame of a new approach in terms of coherent states. Bosons are indeed detected in different physical situations where they exhibit different and apparently…
Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predicts different results for the same physical properties, depending on the ensemble under consideration. Path integral…
The spatial logistic model is a system of point entities (particles) in $\mathbb{R}^d$ which reproduce themselves at distant points (dispersal) and die, also due to competition. The states of such systems are probability measures on the…
Quasi-stationary far-from-equilibrium critical states of a two-component Bose gas are studied in two spatial dimensions. After the system has undergone an initial dynamical instability it approaches a non-thermal fixed point. At this…