Related papers: Order statistics and concentration of l_r norms fo…
In the application of autoregressive models the order of the model is often estimated using either a sequence of likelihood ratio tests, a likelihood based information criterion, or a residual based test. The properties of such procedures…
Let $C$ and $K$ be centrally symmetric convex bodies of volume $1$ in ${\mathbb R}^n$. We provide upper bounds for the multi-integral expression \begin{equation*}\|{\bf…
Two-sided bounds are explored for concentration functions and R\'enyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.
We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in spirit of Talagrand and…
We propose a method for estimating a log-concave density on $\mathbb R^d$ from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave…
In this paper, we consider the log-concave ensemble of random matrices, a class of covariance-type matrices $XX^*$ with isotropic log-concave $X$-columns. A main example is the covariance estimator of the uniform measure on isotropic convex…
We develop concentration inequalities for the $l_\infty$ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-$h$…
Under correlation-type conditions, we derive an upper bound of order $(\log n)/n$ for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved…
We show that the modified log-Sobolev constant for a natural Markov chain which converges to an $r$-homogeneous strongly log-concave distribution is at least $1/r$. Applications include a sharp mixing time bound for the bases-exchange walk…
We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain similar probabilistic estimates for $\ell_p$ norms via real interpolation.
For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…
We study the random variables (r.v.) with values in the so-called mixed (anisotropic) Lebesgue-Riesz spaces: formulate the sufficient conditions for belonging of the r.v. to these spaces, estimate the tail of norms distribution, especially…
In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap…
We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal…
We study the upper tail behaviors of the local times of the additive L\'{e}vy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L_2-norms of the…
We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…
We review some simple techniques based on monotone mass transport that allow to obtain transport-type inequalities for any log-concave probability measure, and for more general measures as well. We discuss quantitative forms of these…
We show that the sequence of moments of order less than 1 of averages of i.i.d. positive random variables is log-concave. For moments of order at least 1, we conjecture that the sequence is log-convex and show that this holds eventually for…
We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of…
We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube in R^n whose density takes the form exp(-H) where the function H is assumed to be…