相关论文: Supersymmetry in Stochastic Quantization Method an…
Determinantal point processes are characterized by a special structural property of the correlation functions: they are given by minors of a correlation kernel. However, unlike the correlation functions themselves, this kernel is not…
We develop an explicit Milstein-type scheme for McKean-Vlasov stochastic differential equations using the notion of derivative with respect to measure introduced by Lions and discussed in \cite{cardaliaguet2013}. The drift coefficient is…
We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we…
Stochastic evolutions of classical field theories have recently become popular in the study of problems such as determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain…
We discuss Stochastic Quantization of $d$=3 dimensional non-Abelian Chern-Simons theory. We demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the…
The scalar field is quantized in the discretized light-front framework following the {\em standard} Dirac procedure and its infinite volume limit taken. The background field and the nonzero mode variables do not commute for finite volume;…
We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the…
We propose a new theoretical approach to ground and low-energy excited states of nuclei extending the nuclear mean-field theory. It consists of three steps: stochastic preparation of many Slater determinants, the parity and angular momentum…
This article describes a new class of prior distributions for nonparametric function estimation. The unknown function is modeled as a limit of weighted sums of kernels or generator functions indexed by continuous parameters that control…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…
This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite step-size…
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…
Covariant stochastic partial (pseudo-)differential equations are studied in any dimension. In particular a large class of covariant interacting local quantum fields obeying the Morchio-Strocchi system of axioms for indefinite quantum field…
In this article, we study a divisor function in an arbitrary number field akin to Koshliakov's work on Vorono\"{\dotlessi} summation formula. More precisely, we generalize Koshliakov's kernel and Koshliakov's transform over any number field…
We rigorously derive a weak form of the Lifshitz-Slyozov-Wagner equation as the homogenization limit of a Stefan-type problem describing reaction-controlled coarsening of a large number of small spherical particles. Moreover, we deduce that…
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…
The Lipatov equation can regarded as a reggeon Bethe-Salpeter equation in which higher-order reggeon interactions give higher-order kernels. Infra-red singular contributions in a general kernel are produced by t-channel nonsense states and…
In this paper we focus on a general type of mean-field stochastic control problem with partial observation, in which the coefficients depend in a non-linear way not only on the state process $X_t$ and its control $u_t$ but also on the…
Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…
We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is…