We present a simple general method for estimating the thickness of heavy tails based on the asymptotics of the sum. The method works for dependent data, and only requires that the centered and normalized partial sums are stochastically compact. For data in the domain of attraction of a stable law our estimator is asymptotically log stable, consistent and asymptotically unbiased, and converges i...

A model for cleaning a graph with brushes was recently introduced. We consider the minimum number of brushes needed to clean d-regular graphs in this model, focusing on the asymptotic number for random d-regular graphs. We use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even) and analyze it using the differential equations method to find the (asymptotic) n...

We build interacting Fock spaces from association schemes and set up quantum walks on the resulting regular graphs (distance-regular distance-transitive). The construction is valid for growing space well defined asymptotically graph. To realize in terms of anyons we switch to dual view identify corresponding modular tensor categories Bose–Mesner algebra. Informally, fusion ring induced by schem...

A twisted hypercube of dimension k is created from two twisted hypercubes of dimension k − 1 by adding a matching joining their vertex sets, with the twisted hypercube of dimension 0 consisting of one vertex and no edges. We generate random twisted hypercube by generating the matchings randomly at each step. We show that, asymptotically almost surely, joining any two vertices in a random twiste...

We show that the largest density of factor of i.i.d. independent sets on the d-regular tree is asymptotically at most (log d)/d as d → ∞. This matches the lower bound given by previous constructions. It follows that the largest independent sets given by local algorithms on random dregular graphs have the same asymptotic density. In contrast, the density of the largest independent sets on these ...

A d-dimensional grid graph G is the graph on a finite subset in the integer lattice Z in which a vertex x = (x1, x2, · · · , xn) is joined to another vertex y = (y1, y2, · · · , yn) if for some i we have |xi − yi| = 1 and xj = yj for all j 6= i. G is hyper-rectangular if its set of vertices forms [K1] × [K2] × · · · × [Kd], where each Ki is a nonnegative integer, [Ki] = {0, 1, · · · , Ki−1}. Th...

Our aim in this paper is to prove some interesting fixed point theorems for the class of asymptotically T-regular mappings framework preordered modular G-metric spaces. results are novel and generalizes several know results. Furthermore we apply our solving nonlinear integral equations.

A ray-optics model is developed to describe the spoiling of the high-Q (whispering gallery) modes of ring-shaped cavities as they are deformed from perfect circularity. A sharp threshold is found for the onset of Q spoiling as predicted by the Kolmogorov-Arnol'd-Moser (KAM) theorem of nonlinear dynamics. Beyond the critical deformation b(c), Q ~ (b - b(c))(-alpha), alpha asymptotically equal to...

For the one-dimensional nonlinear damped Klein-Gordon equation \[ \partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove that any global finite energy solution either converges to $0$ or behaves asymptotically as $t\to \infty$ sum of $K\geq 1$ decoupled solitary waves. In multi-soliton case 2$, ...