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We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We describe various moment-based ensemble interpretation models for the construction of probabilistic temperature forecasts from ensembles. We apply the methods to one year of medium range ensemble forecasts and perform in and out of sample…
We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric…
We develop diffusion models for lattice gauge theories which build on the concept of stochastic quantization. This framework is applied to $U(1)$ gauge theory in $1+1$ dimensions. We show that a model trained at one small inverse coupling…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In…
We present a new framework for the assessment and calibration of medium range ensemble temperature forecasts. The method is based on maximising the likelihood of a simple parametric model for the temperature distribution, and leads to some…
We study a quantum spin system on the $d$-dimensional hypercubic lattice $\Lambda$ with $N=L^d$ sites with periodic boundary conditions. We take an arbitrary translation invariant short-ranged Hamiltonian. For this system, we consider both…
This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…
In this paper we are discussing the question how a continuous quantum system can be simulated by mean field fluctuations of a finite number of qubits. On the kinematical side this leads to a convergence result which states that…
This work investigates the implications of relaxing the measurement independence assumption in Bell's theorem by introducing a new class of local deterministic models that account for both particle preparation and measurement settings. Our…
We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…
The Random Transverse Field Ising Chain is the simplest disordered model presenting a quantum phase transition at T=0. We compare analytically its finite-size scaling properties in two different ensembles for the disorder (i) the canonical…
Predictive states for stochastic processes are a nonparametric and interpretable construct with relevance across a multitude of modeling paradigms. Recent progress on the self-supervised reconstruction of predictive states from time-series…