Related papers: An explicit example for the high temperature convo…
We study the limiting spectral distribution of sample covariance matrices $XX^T$, where $X$ are $p\times n$ random matrices with correlated entries, for the cases $p/n\to y\in [0,\infty)$. If $y>0$, we obtain the Mar\v{c}enko-Pastur…
Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
Let $(M,g)$ be a two-dimensional Riemannian manifold of finite diameter with a conical singularity. Under the assumption that the metric near the cone point $C$ is rotationally invariant, but not necessarily flat, we give an explicit…
We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components,$d,n \ge 1$. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt- or Ibragimov-Linnik-type…
The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been…
We prove that certain families of homogenous affine iterated function systems in $\mathbb{R}^d$ have the property that the open set condition and the existence of exact overlaps both occur densely in the space of translation parameters.…
Having discovered a dimension mistake in two key formulas of the Classical Nucleation Theory (CNT) but wishing to remain in the style of this theory, we propose to approach nucleation on the basis of the Zeldovich unsteady rate formula,…
This work develops a rigorous setting allowing one to prove several features related to the behaviour of the Heisenberg-Ising (or XXZ) spin-$1/2$ chain at finite temperature $T$. Within the quantum inverse scattering method the physically…
We study the adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erd\H{o}s-R\'enyi graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution of the…
About a century ago, Jeans (1919) discovered that if binary stars reach a state approximating energy equipartition, for example through many dynamical encounters that exchange energy, their eccentricity distribution can be described by :…
Turbulent thermals emerge in a wide variety of geophysical and industrial flows, such as atmospheric cumulus convection and pollutant dispersal in oceans and lakes. When a buoyant fluid mass rises, or sinks, heat and mass transfers occur by…
We introduce and study a number of new spaces of ultradifferentiable functions and ultradistributions and we apply our results to the study of the convolution of ultradistributions. The spaces of convolutors…
We propose and test a new method based on Richardson-Lucy deconvolution to reconstruct three-dimensional gas density and temperature distributions in galaxy clusters from combined X-ray and thermal Sunyaev-Zel'dovich observations. Clusters…
We study the thermodynamic and statistical properties of a gas governed by a multifractional modified dispersion relation of the form $\omega^{2}=k^{2}+4E_{*}^{-1/2}k^{5/2}$, where $E_{*}$ sets the characteristic scale of the…
If the thermal evolution of the hot young neutron star in the supernova remnant HESS J1731-347 is driven by neutrino emission, it provides a stringent constraint on the coupling of light (mass $\ll 10$ keV) axion-like particles to neutrons.…
We show that the fraction of time a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by L\'evy for Brownian motion. Stochastic currents with long streaks above or below their average…
A solvable turbulent model is used to predict both the structure of the boundary layer and the scaling laws in thermal convection. The transport of heat depends on the interplay between the thermal, viscous and integral scales of…
Velocity and temperature distributions are both crucial for modeling compressible wall-bounded turbulent flows. The compressible law of the wall for velocity has been extensively examined through velocity transformations. However, a…