相关论文: Large Deviations of the $\Phi^4_3$ Measure via Sto…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
We study a nonlinear stochastic heat equation forced by a space-time white noise on closed surfaces, with nonlinearity $e^{\beta u}$. This equation corresponds to the stochastic quantization of the Liouville quantum gravity (LQG) measure.…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…
We formulate large deviations principle (LDP) for diffusion pair $(X^\epsilon,\xi^\epsilon)=(X_t^\epsilon,\xi_t^\epsilon)$, where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time.…
We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of…
We consider the problem of ergodicity for the $P(\Phi)_2$ measure of quantum field theory under the flow of the singular stochastic (damped) wave equation $u_{tt} + u_t + (1-\Delta) u + {:}\,p(u)\mspace{2mu}{:} = \sqrt 2 \xi$, posed on the…
The climate system is a complex, chaotic system with many degrees of freedom and variability on a vast range of temporal and spatial scales. Attaining a deeper level of understanding of its dynamical processes is a scientific challenge of…
We take the point of view of a particle performing random walk with bounded jumps on $\mathbb{Z}^d$ in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the…
We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…
Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the…
The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory in higher orders. It has been suggested that some of these new features might give rise to a mechanism…
The aim of this paper is to develop tractable large deviation approximations for the empirical measure of a small noise diffusion. The starting point is the Freidlin-Wentzell theory, which shows how to approximate via a large deviation…
We investigate the infinite volume limit of the variational description of Euclidean quantum fields introduced in a previous work. Focussing on two dimensional theories for simplicity, we prove in details how to use the variational approach…
It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order…
This work is concerned with Freidlin-Wentzell type large deviation principle for a family of multi-scale quasilinear and semilinear stochastic partial differential equations. Employing the weak convergence method and Khasminskii's time…
A coarse-grained quantum operator technique is used along with the formalism of Bohmian mechanics endowed with stochastic character at the quantum level in order to address some central issues in the quantum theory of measurement. A…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
We give the generalization of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed both for the Euclidean and Minkowski regions of squared momentum transfer q^2, which takes into account heavy-quark…