Related papers: On the upper bound in Varadhan's Lemma

Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…

A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…

We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…

We generalize and improve the original characterization given by Valadier [20, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove…

Given a Woodin cardinal $\delta$, I show that if $F$ is any Easton function with $F"\delta\subseteq\delta$ and $\GCH$ holds, then there is a cofinality-preserving forcing extension in which $2^\gamma= F(\gamma)$ for each regular cardinal…

We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…

Assuming an averaged form of Mertens' conjecture and that the ordinates of the non-trivial zeros of the Riemann zeta function are linearly independent over the rationals, we analyze the finer structure of the terms in a well-known formula…

The vectorial nonlinearity of a vector valued function is its distance from the set of affine functions. In 2017, Liu, Mesnager and Chen conjectured a general upper bound for the vectorial linearity. Recently, Carlet proved a lower bound in…

We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…

We give a simple and general central limit theorem for a triangular array of m-dependent variables. The result requires only a Lindeberg condition and avoids unnecessary extra conditions that have been used earlier. The result applies also…

Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory.

We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is…

It is proved that the Continuum Hypothesis implies that any sequence of rapid P-points of length $<{\mathfrak c}^{+}$ which is increasing with respect to the Rudin-Keisler ordering is bounded above by a rapid P-point. This is an improvement…

We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…

Let $f$ be a transcendental entire function. The fast escaping set $A(f)$, various regularity conditions on the growth of the maximum modulus of $f$, and also, more recently, the quite fast escaping set $Q(f)$ have all been used to make…

We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function

We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…

In this brief review we will discuss how a well motivated particle theory beyond the eletroweak Standard Model provides ingredients and conditions for a successful inflation. We will mainly focus on a low energy supersymmetric Standard…

Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…