相关论文: Continuum Random Combs and Scale Dependent Spectra…

Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…

We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition properties and controlled singularities. For analytic…

The Randall-Sundrum (RS) model, based on a slice of warped 5D spacetime, was originally introduced to explain the apparent hierarchy between the scales of weak and gravitational interactions. Over the past decade, this model has been…

We review a recently discovered continuum limit for the one-matrix model which describes "causal" two-dimensional quantum gravity. The behaviour of the quantum geometry in this limit is different from the quantum geometry of Euclidean…

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

To facilitate the search for a continuum limit of causal dynamical triangulations, Ambjorn, Coumbe, Gizbert-Studnicki, and Jurkiewicz recently reported measurements of the lattice spacing as a function of the bare couplings. Although these…

The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…

A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of…

This paper studies regression discontinuity designs (RDD) when linear-in-means spillovers occur between units that are close in their running variable. We show that the RDD estimand depends on the ratio of two terms: (1) the radius over…

Quantum-gravity renders the space-time dimension to depend on the size of region; it monotonically increases with the size of region and asymptotically approaches four for large distances. This effect was discovered in numerical simulations…

We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…

Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…

The interplay between cosmology and strongly coupled dynamics can yield transient spectral features that vanish at late times, but which may leave behind phenomenological signatures in the spectrum of primordial fluctuations. Of particular…

We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in 3+1 space-time dimensions starting from over-occupied initial conditions. We determine universal scaling exponents and functions for two-point correlators…

Accurate estimation for extent of cross{sectional dependence in large panel data analysis is paramount to further statistical analysis on the data under study. Grouping more data with weak relations (cross{sectional dependence) together…

The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…

Quantum microcombs generated in high-Q microresonators provide compact, multiplexed sources of entangled modes for continuous-variable (CV) quantum information processing. While deterministic generation of CV states via Kerr-induced…

We consider the contribution to the entropy from fields in the background of a curved time-independent metric. To account for the curvature of space, we postulate a position-dependent UV cutoff. We argue that a UV cutoff on energy naturally…

Chemical imaging enabled by Raman processes is crucial to investigating biological and chemical samples in a label-free manner. Stimulated Raman spectroscopy (SRS) overcomes the key limitation associated with low signal levels in…

We investigate the transition between the phases $B$ and $C_b$ observed in four-dimensional Causal Dynamical Triangulations (CDT). We find that the critical properties of CDT with toroidal spatial topology are the same as earlier observed…