Related papers: Spectral Gap for Measure-Valued Diffusion Processe…
We derive spectral fluctuation--dissipation--response inequalities for finite-state Markov jump processes. By comparing the causal susceptibility to its passive equilibrium reference, we establish frequency-resolved and frequency-integrated…
We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…
We study harmonic measure in finite graphs with an emphasis on expanders, that is, positive spectral gap. It is shown that if the spectral gap is positive then for all sets that are not too large the harmonic measure from a uniform starting…
The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are…
We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for…
In this note, we consider the necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of $R^{m}$ with some concrete examples.
On a measure theoretical dynamical system with spectral gap property we consider non-integrable observables with regularly varying tails and fulfilling a mild mixing condition. We show that the normed trimmed sum process of these…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
Diffusion models excel in content generation by implicitly learning the data manifold, yet they lack a practical method to leverage this manifold - unlike other deep generative models equipped with latent spaces. This paper introduces a…
The points where diffraction orders emerge or vanish in the propagating spectrum of periodic non-Hermitian systems are referred to as scattering thresholds. Close to these branch points, resonances from different Riemann sheets can…
Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…
We study the dependence of the spectral gap for the generator of the Ginzburg-Landau dynamics for all \emph{$\mathcal O(n)$-models} with mean-field interaction and magnetic field, below and at the critical temperature on the number $N$ of…
The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. This paper develops practical applications of spread dimension in the context of machine…
Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
The gap probability generating function has as its coefficients the probability of an interval containing exactly $k$ eigenvalues. For scaled random matrices with orthogonal symmetry, and the interval at the hard or soft spectrum edge, the…
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…
Let $\mu$ be a probability measure on $\rr^n$ ($n \geq 2$) with Lebesgue density proportional to $e^{-V (\Vert x\Vert )}$, where $V : \rr_+ \to \rr$ is a smooth convex potential. We show that the associated spectral gap in $L^2 (\mu)$ lies…
This is the first article in a series of three dealing with the exploitation of speckle for imaging purposes. Speckle is the complex interference wave-field produced by a random distribution of un-resolved scatterers. In this paper, we show…