Sample-to-sample fluctuations in real-network ensembles

Sample to sample fluctuations in the random energy model

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model.

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. He...

Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces.

Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net-neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir force...

Gaussian fluctuations in complex sample covariance matrices

Let X = (Xi,j)m×n,m ≥ n, be a complex Gaussian random matrix with mean zero and variance 1 n , let S = XX be a sample covariance matrix. In this paper we are mainly interested in the limiting behavior of eigenvalues when m n → γ ≥ 1 as n → ∞. Under certain conditions on k, we prove the central limit theorem holds true for the k-th largest eigenvalues λ(k) as k tends to infinity as n → ∞. The pr...

Large sample-to-sample fluctuations of the nonequilibrium critical current through mesoscopic Josephson junctions

We present a theory for the nonequilibrium current in a mesoscopic Josephson junction which is coupled to a normal electron reservoir, and apply it to a chaotic junction. Large sample-to-sample fluctuations of the critical current Ic are found, with rms Ic.ANeD/\ , when the voltage difference eV between the electron reservoir and the junction exceeds the superconducting gap D and the number of ...