Related papers: An Effective Slope Gap Distribution for Lattice Su…
We show that the number of lattice points lying in a thin annulus has a Gaussian value distribution if the width of the annulus tends to zero sufficiently slowly as we increase the inner radius.
We study equidistribution of certain subsets of periodic orbits for subshifts of finite type. Our results solely rely on the growth of these subsets. As a consequence, effective equidistribution results are obtained for both hyperbolic…
Let $\nu$ be a place of a global function field $K$ over a finite field, with associated affine function ring $R_\nu$ and completion $K_\nu$, and let $1 \leq \mathfrak{m}<\textbf{d}$. The aim of this paper is to prove an effective triple…
In a well-known paper by Bruna, Nagel and Wainger [BNW], Fourier transform decay estimates were proved for smooth hypersurfaces of finite line type bounding a convex domain. In this paper, we generalize their results in the following ways.…
We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential,…
We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, $b(y)$, is assumed to be small compared to the scale of the heterogeneities, $L$, but finite. For such "weakly"…
This paper is inspired by Richards' work on large gaps between sums of two squares [10]. It is shown in [10] that there exist arbitrarily large values of $\lambda$ and $\mu$, where $\mu \geq C \log \lambda$, such that intervals $[\lambda,…
We record an alternative proof of a recent joint equidistribution result of Blomer and Michel, based on Ratner's topological rigidity theorem. This approach has the advantage of extending to non-uniform lattices.
In this work, we establish a generalized transfer matrix method that provides exact analytical and numerical solutions for lattice versions of topological models with surface termination in one direction. We construct a generalized…
Let $M=\Gamma\backslash\mathrm{PSL}(2,\mathbb{R})$ be a compact manifold, and let $f\in C^\infty(M)$ be a function of zero average. We use spectral methods to get uniform (i.e. independent of spectral gap) bounds for twisted averages of $f$…
We develop a discrete lattice implementation of the hard thermal loop effective action by the method of added auxiliary fields. We use the resulting model to measure the sphaleron rate (topological susceptibility) of Yang-Mills theory at…
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic…
We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotations axis are…
In this paper we investigate the distribution of the set of values of a linear map at integer points on a quadratic surface. In particular, it is shown that subject to certain algebraic conditions, this set is equidistributed. This can be…
We provide a self-contained, accessible introduction to Ratner's Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution result was first obtained in the early…
The unstable foliation, that locally is given by changing horizontal components of period coordinates, plays an important role in study of translation surfaces, including their deformation theory and in the understanding of horocycle…
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron…
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and…
The overlap formalism of chiral fermions provides a tool to measure the index, Q, of the chiral Dirac operator in a fixed gauge field background on the lattice. This enables a numerical measurement of the probability distribution, p(Q), in…
A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations…