Related papers: Space-time random walk loop measures
We explore the free boson unitary dynamics subject to repeated random forced measurement. The input state is chosen as a Fock state in real space with the particle number conserved in the entire dynamics. We show that each boson is…
The random convex hull of a Poisson point process in $\mathbb{R}^d$ whose intensity measure is a multiple of the standard Gaussian measure on $\mathbb{R}^d$ is investigated. The purpose of this paper is to invent a new viewpoint on these…
The interdependence of position and momentum, as highlighted by the Heisenberg uncertainty principle, is a cornerstone of quantum physics. Yet, position-momentum correlations have received little systematic attention. Motivated by recent…
We study the finiteness of physical measures for skew-product transformations $F$ associated with discrete-time random dynamical systems driven by ergodic Markov chains. We develop a framework, using an independent and identically…
Recently, in ["The coin-turning walk and its scaling limit", Electronic Journal of Probability, 25 (2020)], the ``coin-turning walk'' was introduced on ${\mathbb Z}$. It is a non-Markovian process where the steps form a (possibly)…
This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system…
In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a…
Anisotropic measurements of the Baryon Acoustic Oscillation (BAO) feature within a galaxy survey enable joint inference about the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$. These measurements are typically obtained from…
The physical origin of spacetime discreteness remains a central open problem in quantum gravity, with most existing approaches relying on specific microscopic structures or model-dependent assumptions. In this letter, spacetime discreteness…
This paper is a continuation of the author's companion work \cite{InoueQuasi} on Haar-type measures for topological quasigroups, where the quasigroup setting was analyzed in connection with Kunen's theorem. We extend that framework to…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
We establish the existence of generalized Busemann functions and Gibbs-Dobrushin-Landford-Ruelle measures for a general class of lattice random walks in random potential with finitely many admissible steps. This class encompasses directed…
We present a method for computing the non-perturbative mass-gap in the theory of Bosonic membranes in flat background spacetimes with or without background fluxes. The computation of mass-gaps is carried out using a matrix regularization of…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
A new procedure of the linear position measurement which allows to obtain sensitivity better than the Standard Quantum Limit and close to the Energetic Quantum Limit is proposed and analyzed in details. Proposed method is based on the…
A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…
Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of…
We show exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under finite first moment condition, and establish the dimension formula by the entropy over the drift. We also treat the…
In this paper, we study Markovian random iterations of maps on standard measurable spaces. We establish a one-to-one correspondence between stationary measures and a certain class of invariant measures of a Markovian random iteration,…
In this paper, we present a unified approach to establish the uniqueness of generalized conformal restriction measures with central charge $c \in (0, 1]$ in both chordal and radial cases, by relating these measures to the Brownian loop…