Related papers: A Berry-Esseen Bound for Quantum Lattice Systems
Understanding the asymptotic behavior of physical quantities in the thermodynamic limit is a fundamental problem in statistical mechanics. In this paper, we study how fast the eigenstate expectation values of a local operator converge to a…
We introduce a new family of distributions to approximate $\mathbb {P}(W\in A)$ for $A\subset\{...,-2,-1,0,1,2,...\}$ and $W$ a sum of independent integer-valued random variables $\xi_1$, $\xi_2$, $...,$ $\xi_n$ with finite second moments,…
We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state…
We discuss the issue of measuring the mean position (center-of-mass) of a group of bosonic or fermionic quantum particles, including particle number fluctuations. We introduce a standard quantum limit for these measurements at ultra-low…
We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied…
We prove the second law of thermodynamics and the nonequilibirum fluctuation theorem for pure quantum states.The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but…
Statistical mechanics harmonizes mechanical and thermodynamical quantities, via the notion of local thermodynamic equilibrium (LTE). In absence of external drivings, LTE becomes equilibrium tout court, and states are characterized by…
We analyze the quality of the gaussian approximation to linear combinations of n independent, identically-distributed random variables with finite fourth moments. It turns out that there exist universal, simple linear combinations that…
We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…
We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary…
A useful heuristic in the understanding of large random combinatorial structures is the Arratia-Tavare principle, which describes an approximation to the joint distribution of component-sizes using independent random variables. The…
A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we study a setting where relaxation to a steady state is exact,…
We prove the Central Limit Theorem for the Euler-Poincar\'e characteristic of Berry's random wave model in a growing domain. We also show Gaussian fluctuations for a class of Berry's mixture models that correspond to a perturbation of the…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
Under natural assumptions on the observable, we prove a Central Limit Theorem, a Berry-Esseen Theorem, and a quantitative Local Limit Theorem for a broad class of partially hyperbolic endomorphisms of the two-dimensional torus. Our results…
The inductive size bias coupling technique and Stein's method yield a Berry-Esseen theorem for the number of urns having occupancy $d \ge 2$ when $n$ balls are uniformly distributed over $m$ urns. In particular, there exists a constant $C$…
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed positive random $d\times d$ matrices and consider the matrix product $G_n: = g_n \ldots g_1$. Under suitable conditions, we establish the Berry-Esseen bounds…
Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum…
Let $\mu$ be a probability measure on $\text{GL}_d(\mathbb R)$ and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$'s are i.i.d.'s with law $\mu$. We study statistical properties of random variables of the…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…