Modeling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains

Sample to sample fluctuations in the random energy model

Finite sample effects in vector autoregressive modeling

In vector autoregressive modeling, the order selected with the Akaike Information Criterion tends to be too high. This effect is called overfit. Finite sample effects are an important cause of overfit. By incorporating finite sample effects, an order selection criterion for vector AR models can be found with an optimal trade-off of underfit and overfit. The finite sample formulae in this paper ...

Sample Path Large Deviations for a Class of Markov Chains Related to Disordered Mean Field Models

We prove a large deviation principle on path space for a class of discrete time Markov processes whose state space is the intersection of a regular domain Λ ⊂ R with some lattice of spacing ǫ. Transitions from x to y are allowed if ǫ−1(x−y) ∈ ∆ for some fixed set of vectors ∆. The transition probabilities pǫ(t, x, y), which themselves depend on ǫ, are allowed to depend on the starting point x a...

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...

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 ...