Related papers: Fluctuating Ensemble Averages and the BTZ Threshol…
An important question about black holes is to what extent a typical pure state differs from the ensemble average. We show that this question can be answered within semi-classical gravity. We focus on the quantum deviation, which measures…
In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the effects of averaging over an ensemble of…
We consider the ensemble average of two dimensional symmetric product orbifold CFTs $\text{Sym}^N(\mathbb{T}^D)$ over the Narain moduli space. We argue for a bulk dual given by $N$ copies of an abelian Chern-Simons theory coupled to…
We develop an alternative approach to this field, which was to a large extent developed by Verbeure et al. It is meant to complement their approach, which is largely based on a non-commutative central limit theorem and coordinate space…
We discuss the interrelations between several ideas in quantum gravity -- holography, the Swampland, and the concept of ensemble averaging. To do so, we study ensemble averages of Narain-type theories associated with general even quadratic…
We explore how to detect the large quantum fluctuations in the throat of a near-extremal black hole, where the dynamics are governed by the Schwarzian theory. To this end, we scatter a low-frequency wave of a massless, minimal scalar off…
Subensemble is a type of statistical ensemble which is the generalization of grand canonical and canonical ensembles. The subensemble acceptance method (SAM) provides general formulas to correct the cumulants of distributions in heavy-ion…
We investigate the impact of oscillations of a black-hole mass around its average value on the three-dimensional black hole geometry. Drawing on a classical framework that conceptualizes fluctuations near an event horizon as mass…
The gravitational path integral produces an asymptotic expansion in $G_N$, a fact which is puzzling in the case of observables that are expected to fluctuate wildly. Wormholes appear to compute ensemble averages of functions of such…
In this paper, we consider the effect of thermal fluctuations on the entropy of both neutral and charged black holes. We emphasize the distinction between fixed and fluctuating charge systems; using a canonical ensemble to describe the…
Supersymmetric rotating 1/16-BPS black holes in $AdS_4 \times S^7$ are expected to capture the average degeneracy of BPS states in the dual ABJM superconformal theory for given fixed charges. This has been successfully demonstrated for the…
The general fluctuation theory is reviewed with special attention to the role played by different ensembles, and is extended to incorporate stationary metastable states obtained in the long time limit. The fluctuation in a quantity depends…
Exploring the universal structure of the gravitational path integral beyond semi-classical saddles and uncovering a compelling statistical interpretation of black hole thermodynamics have long been significant challenges. We investigate the…
Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from…
In this paper, we investigate the second-order normal quantum fluctuation on the world-sheet of a probe string in the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. These fluctuations is treated as the projection of Hawking radiation on the…
Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…
Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average $v(\Delta t)$ and the standard deviation $\delta v(\Delta t)$ of the variance $v[\mathbf{x}]$ of time…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…
We study global fluctuations for singular values of $M$-fold products of several right-unitarily invariant $N \times N$ random matrix ensembles. As $N \to \infty$, we show the fluctuations of their height functions converge to an explicit…