Related papers: Finite range Decomposition of Gaussian Processes

We consider a lattice gas in spaces of dimensionality $\mathcal{D}=1,2,3$. The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in…

One of the most beautiful results in the integral representation theory of finite groups is a theorem of A. Weiss that detects a permutation $R$-lattice for the finite $p$-group $G$ in terms of the restriction to a normal subgroup $N$ and…

We study lattices in a product $G = G_1 \times \dots \times G_n$ of non-discrete, compactly generated, totally disconnected locally compact (tdlc) groups. We assume that each factor is quasi just-non-compact, meaning that $G_i$ is…

A finite subset $K$ of $\mathbb{Z}^d$ is said to be lattice-convex if $K$ is the intersection of $\mathbb{Z}^d$ with a convex set. The covariogram $g_K$ of $K\subseteq \mathbb{Z}^d$ is the function associating to each $u \in \integer^d$ the…

Convergence of the Gauss resolution process for a complex singular foliation of dimension r is shown to be equivalent to finite type of a graded sheaf which is built using base (r+2) expansions of integers. As applications it is calculated…

We prove stability bounds for local gauge-invariant scalar QCD quantum models, with multiflavored bosons replacing (anti)quarks. We take a compact, connected gauge Lie group G, and concentrate on G=U(N),SU(N). Let d(N)=N^2,(N^2-1) be their…

Let $G$ be a connected semisimple Lie group with finite centre and $K$ be a maximal compact subgroup thereof. Given a function $u$ on $G$, we define $\mathcal{A} u$ to be the root mean square average over $K$, acting both on the left and…

We study the canonical solution of a family of classical $n-vector$ spin models on a generic $d$-dimensional lattice; the couplings between two spins decay as the inverse of their distance raised to the power $\alpha$, with $\alpha<d$. The…

In this paper, we study lattice gauge theory on \( \mathbb{Z}^4 \) with finite Abelian structure group. When the inverse coupling strength is sufficiently large, we give an upper bound on the decay of correlations of local functions and…

We present a general form of Renormalization operator $\mathcal{R}$ acting on potentials $V:\{0,1\}^\mathbb{N} \to \mathbb{R}$. We exhibit the analytical expression of the fixed point potential $V$ for such operator $\mathcal{R}$. This…

The general d-dimensional twisted group lattice is solved. The irreducible representations of the corresponding group are constructed by an explicit procedure. It is proven that they are complete. All matrix representation solutions to the…

We present an infinite lattice DMRG sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct…

We establish a duality for two factorization questions, one for general positive definite (p.d) kernels $K$, and the other for Gaussian processes, say $V$. The latter notion, for Gaussian processes is stated via Ito-integration. Our…

We continue our investigation of the Gauss variational problem for infinite dimensional vector measures associated with a condenser $(A_i)_{i\in I}$. It has been shown in Potential Anal., DOI:10.1007/s11118-012-9279-8 that, if some of the…

Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme, if not accurate…

Learning expressive kernels while retaining tractable inference remains a central challenge in scaling Gaussian processes (GPs) to large and complex datasets. We propose a scalable GP regressor based on deep basis kernels (DBKs). Our DBK is…

There exist lattice actions which give cut--off independent physical predictions even on coarse grained lattices. Rotation symmetry is restored, the spectrum becomes exact and, in addition, the classical equations have scale invariant…

The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the one-dimensional lattice expressed through Euler's Gamma function. The Gamma kernel depends on two continuous…

This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation…

Let G be a discrete group which acts properly and isometrically on a complete CAT(0)-space X. Consider an integer d with d=1 or d greater or equal to 3 such that the topological dimension of X is bounded by d. We show the existence of a…