Related papers: Quantum Large Deviations

We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures…

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…

Using the tools of q--differential calculus and quantum Lie algebras associated to quantum groups, we find a one--parameter family of q-gauge theories associated to the quantum group $ISO_q(3,1)$. Although the gauge fields, that is the…

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.

Let $({\mathcal{T}}_{*t})$ be a predual quantum Markov semigroup acting on the full 2 x 2 matrix algebra and having an absorbing pure state. We prove that for any initial state $\omega$, the net of orthogonal measures representing the net…

It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets…

This work extends the variance reduction method for the pricing of possibly path-dependent derivatives, which was developed in (Genin and Tankov, 2016) for exponential L\'evy models, to affine stochastic volatility models (Keller-Ressel,…

A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…

This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…

We consider the divergences in quantum electrodynamics. Our approach is based on ideas from the theory of generalized wave operators. In particular, we use the concept of the deviation factor. The deviation factor characterizes the…

We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates, that are consistent with central limit…

In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are…

$\Psi$-epistemic models of quantum mechanics imply that the quantum state does not correspond to physical reality, but instead reflects the observer's knowledge of the underlying quantum system. The epistemic view of the quantum state has…

In order to account for possible nonstatistical fluctuations in a hadronizing system (leading to the characteristic power-like behavior of the respective single particle spectra and to the broadening of the corresponding multiparticle…

We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This…

In this article we show that the empirical measure of certain continuous time random walks satisfies a strong large deviation principle with respect to a topology introduced in~\cite{MV2016} by Mukherjee and Varadhan. This topology is…

We prove a quantified Tauberian theorem involving Laplace-Stieltjes transform which is motivated by the work of Ingham and Karamata. For this, we consider functions which are locally of bounded variation and, therefore, get a generalisation…

We present a proof of the central limit theorem for a pair of mutually non-commuting operators in mixing quantum spin chains. The operators are not necessarily strictly local but quasi-local. As a corollary we obtain a direct construction…

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…

Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 large deviation {\em functional} characterizing the empirical density of the underlying…