Related papers: Dimension walks on $\mathbb{S}^d \times \mathbb{R}…

Using a structure theorem from [FG2010] we prove a version of multiple recurrence for sets of positive measure in a general stationary dynamical system.

Spherically symmetric random walks in arbitrary dimension $D$ can be described in terms of Gegenbauer (ultraspherical) polynomials. For example, Legendre polynomials can be used to represent the special case of two-dimensional spherically…

We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an analytic capability similar to that contributed by the z…

We study the function $(1 - \|x\|)\slash (1 - \|x\|^r),$ and its reciprocal, on the Euclidean space $\mathbb{R}^n,$ with respect to properties like being positive definite, conditionally positive definite, and infinitely divisible.

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…

We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n-1}$. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded…

We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the…

This paper is a sequel to Chaika and Krishnan [arXiv:1612.00434]. We again consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice Z^d. We assume that once walks meet, they…

We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the…

We prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under…

We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability $\theta$ and with probability $1 - \theta$, the random walk performs a step independent of the past. We analyse its asymptotic…

We consider (random) walks in a multidimensional orthant. Using the idea of universality in probability theory, one can associate a unique polyhedral domain to any given walk model. We use this connection to prove two sets of new results.…

We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical - the discrete-time Polya walk, in which the walker steps at each integer moment of time, and…

Let $W_d(n)$ be the number of $2n$-step walks in $\mathbb{Z}^d$ which begin and end at the origin. We study the exponent of $2$ in the prime factorisation of this number; i.e., $w_d(n) = \nu_2(W_d(n))$. We show that, for each $d$, there is…

We observe that an analogue of the Positive Mass Theorem in the time-symmetric case for three-space-time-dimensional general relativity follows trivially from the Gauss-Bonnet theorem. In this case we also have that the spatial slice is…

Given $d\geq2$, we construct a Zariski-dense random walk on the space of lattices SL$_d(\mathbb{R})/$SL$_d(\mathbb{Z})$ that exhibits escape of mass. This negates the suggestion of recurrence made by Benoist [Ben14] (ICM 2014) and by…

A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…

We define a random walk on the set of primitive points of $\mathbb{Z}^d$. We prove that for walks generated by measures satisfying mild conditions these walks are recurrent in a strong sense. That is, we show that the associated Markov…

For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a…

We give an overview of the correspondance between one-time-physics and two-time-physics. This is characterized by the presence of an SO(d,2) symmetry and an Sp(2) duality among diverse one-time-physics systems all of which can be lifted to…