arXiv research

Establishes Calderón-Zygmund inequalities on evolving Riemannian manifolds.

Improved analysis of UCRL2 with empirical Bernstein inequality reduces exploration-exploitation regret.

New inequality for ternary variables improves on existing measures.

Sharp bounds for curve isoperimetric deficit derived.

The paper finds new inequalities for convex polygons.

Unified approach to discrete and smooth isoperimetric inequalities of arbitrary order.

Note on failure of Martingale Wasserstein Inequality in higher dimensions.

New method proves inequalities for self-shrinkers using perturbation.

The study examines how quadratic inequalities affect distances in length spaces.

Sharp inequalities and extremals on compact Riemann surfaces with boundary.

This research quantifies cross-sectoral inequalities using latent class analysis.

Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…

Unified analysis of efficient local training methods for distributed variational inequalities.

This is a survey article on recent progress of comparison geometry and geometric analysis on Finsler manifolds of weighted Ricci curvature bounded below. Our purpose is two-fold: Give a concise and geometric review on the birth of weighted Ricci curvature and its applications; Explain recent results from a nonlinear an…

Probability versions of Li-Yau inequalities for manifolds with boundary.

The paper addresses geometric analysis on non-compact Riemannian manifolds, proving Calderón-Zygmund inequalities.

This paper extends the convergence analysis of Langevin Monte Carlo beyond Poincaré inequalities.

Sharp inequalities on Siegel domains and complex hyperbolic spaces established.

New method uses entropy dissipation to prove isoperimetric inequalities.

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…

The Minkowski inequality is a classical inequality in differential geometry, giving a bound from below, on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving versions of this inequality for manifolds other than R^n; for example, such an ine…

Proves conjectured capillary Blaschke-Santaló inequality for certain convex hypersurfaces.

We continue our study of geometric analysis on (possibly non-reversible) Finsler manifolds, based on the Bochner inequality established by the author and Sturm. Following the approach of the $Γ$-calculus a la Bakry et al, we show the dimensional versions of the Poincare--Lichnerowicz inequality, the logarithmic Sobolev…

Paper proves inequality for capillary hypersurfaces in a wedge.

New concentration inequalities for tensors with heavy-tailed coefficients.

The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.

The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincaré inequalities. Typically two kind of sensitivity indices are linked by a Poincaré type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper …

The study shows that close hypersurfaces have uniformly bounded inequalities.

Sharp inequalities and symmetries on Riemannian surfaces quantified.

Proof of reverse isoperimetric inequality for black holes.

This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of k-generalized statistics, is derived that is particularly suitable to describe the whole spectrum of incomes, from the low-middle income region up…

Sharp stability results for reverse isoperimetric inequalities in 2D.

Given a probability measure $μ$ supported on a convex subset $Ω$ of Euclidean space $(\mathbb{R}^d,g_0)$, we are interested in obtaining Poincaré and log-Sobolev type inequalities on $(Ω,g_0,μ)$. To this end, we change the metric $g_0$ to a more general Riemannian one $g$, adapted in a certain sense to $μ$, and perform…

New inequalities help optimize first-order algorithms for statistical risk analysis.

New approach to concentration inequalities for unbounded state space dynamical systems.

This paper identifies the salient factors that characterize the inequality income distribution for Romania. Data analysis is rigorously carried out using sophisticated techniques borrowed from classical statistics (Theil). Decomposition of the inequalities measured by the Theil index is also performed. This study relie…

Black women and white men have the highest income disparity in the U.S.

This paper examines challenges and solutions for solving variational inequalities.

Solved Cheeger inequalities for simplicial complexes, combining topological and graph theoretic methods.

We consider an abstract compact orientable Cauchy-Riemann manifold endowed with a Cauchy-Riemann complex line bundle. We assume that the manifold satisfies condition Y(q) everywhere. In this paper we obtain a scaling upper-bound for the Szegö kernel on (0, q)-forms with values in the high tensor powers of the line bund…

A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.

Uniform Sobolev inequality for Kähler metrics with entropy bound.

Quantifies nearly spherical subsets in complex ball geometry.

Proves inequality linking function deviation to gradient norm on compact manifolds.

The paper proves concentration inequalities for diffusion processes.

New concentration inequality for U-statistics of Markov chains.

This paper concerns conditions related to the first finite singularity time of a Ricci flow solution on a closed manifold. In particular, we provide a systematic approach to the mean value inequality method, suggested by N. Le and F. He. We also display a close connection between this method and time slice analysis of …

We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…