相关论文: Gaussian, Mean Field and Variational Approximation…
We study the scaling limit and prove the law of large numbers for weakly pinned Gaussian random fields under the critical situation that two possible candidates of the limits exist at the level of large deviation principle. This paper…
We give a review of the exact renormalization group (ERG) approach and illustrate its applications in scalar and fermionic theories. The derivative expansion and approximations based on the derivative expansion with further truncation in…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by…
We consider light scalar fields during inflation and show how the stochastic spectral expansion method can be used to calculate two-point correlation functions of an arbitrary local function of the field in de Sitter space. In particular,…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…
Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\lambda$. The inputs are the classical…
We prove that any scaling limit of a critical reflection positive Ising or $\varphi^4$ model of effective dimension $d_{\text{eff}}$ at least four is Gaussian. This extends the recent breakthrough work of Aizenman and Duminil-Copin -- which…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
We consider massive \lambda\phi^4 theory in de Sitter background. The mass of the scalar field \phi is chosen small enough, such that the amplification of superhorizon momentum modes leads to a significant enhancement of infrared…
To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the…
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting…
We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective…
We evaluate the thermal corrections to the generalized Gaussian effective potential. We carry out the calculations of the lowest order corrections in the case of self-interacting scalar fields in one and two spatial dimensions, and study…
We analyze high-temperature series expansions of the two-point and four-point correlation-functions in the three-dimensional euclidean lattice scalar field theory with quartic self-coupling, which have been recently extended through…
Recently, non-perturbative approximate solutions were presented that go beyond the well-known mean-field resummation. In this work, these non-perturbative approximations are used to calculate finite temperature equilibrium properties for…