Related papers: Volume and heat kernel fluctuations for the three-…
Given a Gaussian analytic function $f_L$ of intesity $L$ in the unit ball of $\mathbb C^n$, $n\geq 2$, consider its (random) zero variety $Z(f_L)$. We study the variance of the $(n-1)$-dimensional volume of $Z(f_L)$ inside a…
We consider time-dependent random walks among time-dependent conductances. For discrete time random walks, we show that, unlike the time-independent case, two-sided Gaussian heat kernel estimates are not stable under perturbations. This is…
We propose an Ansatz for Universal conductance fluctuations in continuous dimensions from 0 up to 4. The Ansatz agrees with known formulas for integer dimensions 1, 2 and 3, both for hard wall and periodic boundary conditions. The method is…
Quantum fluctuation of the energy is studied for an ultracold gas of interacting fermions trapped in a three-dimensional potential. Periodic-orbit theory is explored, and energy fluctuations are studied versus particle number for generic…
Relativistic particle production often requires the use of Tsallis statistics to account for the apparently power-like behavior of transverse momenta observed in the data even at a few GeV/c. In such an approach this behavior is attributed…
We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calulations in the plane and on the sphere.…
The pumping conductance of a disordered two-dimensional Chern insulator scales with increasing size and fixed disorder strength to sharp plateau transitions at well-defined energies between ordinary and quantum Hall insulators. When the…
Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either…
Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that…
We study the invariant distributions of Hammersley's serial harness process in all dimensions and height fluctuations in one dimension. Subject to mild moment assumptions there is essentially one unique invariant distribution, and all other…
Let $\mathcal{U}$ be the uniform spanning tree on $\mathbb{Z}^3$, whose probability law is denoted by $\mathbf{P}$. For $\mathbf{P}$-a.s. realization of $\mathcal{U}$, the recurrence of the the simple random walk on $\mathcal{U}$ is proved…
Thermodynamic quantities, like heat, entropy, or work, are random variables, in stochastic systems. Here, we investigate the statistics of the heat exchanged by a Brownian particle subjected to a logarithm-harmonic potential. We derive…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
We study the stochastic heat flow with constant initial data and analyze its spatial average on the scale of $\varepsilon\ll1$. We prove that the logarithm of the averaged process satisfies a pointwise central limit theorem: After being…
There is a special relation between the spectrum and the {\it truncated} heat kernel of the Euclidean BTZ black hole with the Patterson-Selberg zeta function. Using an orbifold description of this relation we calculate the on-shell…
We investigate the number fluctuations in small cells of quantum gases pointing out important deviations from the thermodynamic limit fixed by the isothermal compressibility. Both quantum and thermal fluctuations in weakly as well as highly…
We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded…
We study, by means of extensive direct numerical simulations, the turbulent flow produced by a two-dimensional cellular forcing in a cubic box with periodic boundary conditions. In spite of the strong anisotropy of the forcing, we find that…
We have studied numerically the fluctuations of the conductance, $g$, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of $\ln g$ varies with the lateral sample…
We study the effects of thermal fluctuations on a small elastic ring. We derive analytical expressions for the correlation functions of the Euler angles, for the real space two--point correlation functions and for the probability…