Related papers: Self-averaging in random systems - liability or as…
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between…
The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of…
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Recent renormalization group results predict non self averaging behaviour at criticality for relevant disorder. However, we find strong self averaging(SA) behaviour in the critical region of a quenched Ising model on an ensemble of…
The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in…
The spectral form factor, k(t), is the Fourier transform of the two level correlation function C(x), which is the averaged probability for finding two energy levels spaced x mean level spacings apart. The average is over a piece of the…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
Randomness is ubiquitous in many applications across data science and machine learning. Remarkably, systems composed of random components often display emergent global behaviors that appear deterministic, manifesting a transition from…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
We consider distributed iterative algorithms for the averaging problem over time-varying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
We consider quenches in non-conserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
First order phase transitions proceed via nucleation. The rate of nucleation varies exponentially with the free-energy barrier to nucleation, and so is highly sensitive to variations in this barrier. In practice, very few systems are…
This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we…
We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects of quenched bond randomness on the self-averaging properties of two Ising spin models in 2d. The random bond version of the superantiferromagnetic (SAF) square…
We present methods and results of shot-by-shot correlation of noisy measurements to extract entangled state and process tomography in a superconducting qubit architecture. We show that averaging continuous values, rather than counting…
We investigate global phase coherence in a system of coupled oscillators on a small-world networks constructed from a ring with nearest-neighbor edges. The effects of both thermal noise and quenched randomness on phase ordering are examined…
Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…