Related papers: Finitary coding and Gaussian concentration for ran…
We consider spin-flip dynamics of configurations in $\{-1,1\}^{\mathbb{Z}^d}$, and study the time evolution of concentration inequalities. For "weakly interacting" dynamics we show that the Gaussian concentration bound is conserved in the…
In this paper we show that any sequence of infinite lattice constellations which is good for the unconstrained Gaussian channel can be shaped into a capacity-achieving sequence of codes for the power-constrained Gaussian channel under…
Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…
We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also known as "chains with complete connections" or "$g$-measures". We consider…
We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer science, and learning theory. In this paper, we consider centered…
We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under…
The finitary isomorphism theorem, due to Keane and Smorodinsky, raised the natural question of how "finite" the isomorphism can be, in terms of moments of the coding radius. More precisely, for which values does there exist an isomorphism…
We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the…
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…
We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds…
We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters,…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
Spectral properties of Gram matrices are central to high dimensional asymptotic analyses of statistical estimators in regression and covariance estimation. These properties, in turn, depend critically on the extreme singular values and…
We consider the behavior of the Gaussian concentration bound (GCB) under stochastic time evolution. More precisely, we consider a Markovian diffusion process on $\mathbb{R}^d$ and start the process from an initial distribution $\mu$ that…
A new method of employing an isospin chemical potential for QCD-like theories with different number of colors, number of fermion flavors, and in different fermion representations is proposed. The isospin chemical potential, which can be…
This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…