Related papers: Determinant Calculations Using Random Walk Worldli…
A possibility is discussed for experimental testing of the dark matter model supported by a classic non-Abelian SU(3) gauge (Yang-Mills) field. Our approach is based on the analysis of the motion of color-charged particles on the background…
The calculation of scattering amplitudes in Yang-Mills theory at loop level is important for the analysis of background processes at particle colliders as well as our understanding of perturbation theory at the quantum level. We present…
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which…
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by…
We calculate explicit speeds for random walks in uniform degenerate random environments. For certain non-uniform random environments, we calculate speeds that are non-monotone.
There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant…
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…
We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
We identify a universal finite-$N$ structure underlying Wilson loop expectations in lattice Yang-Mills, in any dimension $d\geq 2$, for gauge group $\mathrm{U}(N)$, and for arbitrary smooth central plaquette actions. The starting point is a…
In our previous publications we have developed some elements of Noncommutative calculus on the enveloping algebras of $A_m$ type, in particular, analogs of the partial derivatives and de Rham complex were defined. Also, we introduced the…
The dynamics of Wilson loops are governed by an infinite set of Schwinger-Dyson equations and trace relations. In the context of the lattice positivity bootstrap, a central challenge is determining a dynamically independent basis of these…
This document contains supplementary material for the main articles in our Random Cayley Graphs project. We prove refined results about simple random walks on the integers and on the cycle. We are primarily interested in the entropy of…
We study the path behavior of the symmetric walk on some special comb-type subsets of ${\mathbb Z}^2$ which are obtained from ${\mathbb Z}^2$ by generalizing the comb having finitely many horizontal lines instead of one.
We study the path behavior of the simple symmetric walk on some comb-type subsets of Z^2 which are obtained from Z^2 by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation…
A formula expressing the fermionic determinant as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and are indexed by loops of…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
We employ the Transformer to learn patterns in two-dimensional lattice Yang-Mills theory. Specifically, we represent both Wilson loops and their expectation values as tokenized sequences. Taking the shape of Wilson loops as input, the model…
A method is described to count simple diagonal walks on $\mathbb{Z}^2$ with a fixed starting point and endpoint on one of the axes and a fixed winding angle around the origin. The method involves the decomposition of such walks into smaller…
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…