Related papers: Link-based causal set propagators in $1+1$ dimensi…
The coincidence limits of the massless, minimally coupled scalar propagator and its first two derivatives have great relevance for the project of summing up the leading logarithms induced by loops of inflationary gravitons. We use…
Given that the free massive scalar propagator in 2 + 1 dimensional Euclidean space is $D(x-y)=\frac{1}{4\pi \rho} 0.25cm e^{-m \rho} $ with $\rho^2=(x-y)^2$ we present the counterpart of $D(x-y)$ in curved space with a suitably modified…
We suggest a new hardcore Poisson-type distribution for Young diagrams with the row lengths from some finite list. A discrete variant of the time-ordered Mat\'{e}rn II process in 1D is employed. This approach is related to that based on the…
Designing mechanical linkages to achieve target end-effector trajectories presents a fundamental challenge due to the intricate coupling between continuous node placements, discrete topological configurations, and nonlinear kinematic…
This is the first of two subsequent publications where the probability distribution of delay-times in scattering of wave packets is discussed. The probability distribution is expressed in terms of the on-shell scattering matrix, the…
We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to…
We consistently develop a recently proposed scheme of matrix extension of dispersionless integrable systems for the general case of multidimensional hierarchies, concentrating on the case of dimension $d\geqslant 4$. We present extended Lax…
The invariant imbedding evolution equations for the amplitude reflection and transmission coefficients of a disordered 1D chain are shown to follow from the continuum limit, for weak disorder, of recursion relations between reflection…
This paper proposes a debiased estimator for causal effects in high-dimensional generalized linear models with binary outcomes and general link functions. The estimator augments a regularized regression plug-in with weights computed from a…
We show that the Feynman propagator (or the d'Alembertian) of a causal set contains the complete information about the causal set. Intuitively, this is because the Feynman propagator, being a correlator that decays with distance, provides a…
We equip the polytope of $n\times n$ Markov matrices with the normalized trace of the Lebesgue measure of $\mathbb{R}^{n^2}$. This probability space provides random Markov matrices, with i.i.d. rows following the Dirichlet distribution of…
We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a…
Classical sequential growth models for causal sets provide an important step towards the formulation of a quantum causal set dynamics. The covariant observables in a class of these models known as generalised percolation have been…
I define the lattice propagator on a very general collection of graphs, namely graphs locally isomorphic to $\mathbb{Z}^{d}\times \mathbb{Z}$. I then define polygonal approximations to the minkowski metric and define a corresponding lattice…
An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form…
For the first time, as far as we know, in field theory are found explicit forms of propagators satisfying the K\"allen -- Lehmann representation. To be exact, it is shown that scalar meson propagators, taking into account a virtual…
We have obtained propagators in the position space as an expansion over Landau levels for the charged scalar particle, fermion, and massive vector boson in a constant external magnetic field. The summation terms in the resulting expressions…
In this paper, we study the empirical spectral distribution of Spearman's rank correlation matrices, under the assumption that the observations are independent and identically distributed random vectors and the features are correlated. We…
Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under…
The renormalized Feynman propagator for a scalar field in the background of a cosmic dispiration (a disclination plus a screw dislocation) is derived, opening a window to investigate vacuum polarization effects around a cosmic string with…