Related papers: Concentration of Haar measures, with an applicatio…

Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Pek\"oz, R\"ollin, and Ross (2016, arXiv:1309.4183 [math.PR]) exploited characterizing distributional fixed…

Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…

In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many…

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…

We consider a random walk $S_k$ with i.i.d. steps on a compact group equipped with a bi-invariant metric. We prove quantitative ergodic theorems for the sum $\sum_{k=1}^N f(S_k)$ with H\"older continuous test functions $f$, including the…

While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive…

An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…

We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…

We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries…

We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields…

Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

We present new explicit upper bounds for the smoothness of the distribution of the random diagonal sum $S_n=\sum_{j=1}^nX_{j,\pi(j)}$ of a random $n\times n$ matrix $X=(X_{j,r})$, where the $X_{j,r}$ are independent integer valued random…

Measuring treatment efficacy in mixture of subgroups from a randomized clinical trial is a fundamental problem in personalized medicine development, in deciding whether to treat the entire patient population or to target a subgroup. We show…

In this paper, we analyse a sub-class of two-dimensional homogeneous nearest neighbour (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the…

The tails of the distribution of a mean zero, variance $\sigma^2$ random variable $Y$ satisfy concentration of measure inequalities of the form $\mathbb{P}(Y \ge t) \le \exp(-B(t))$ for $$ B(t)=\frac{t^2}{2( \sigma^2 + ct)} \quad \mbox{for…

We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high…

Considering a general framework of bootstrap with exchangeable weights, we show some concentration inequalities for the supremum of the bootstrap empirical process. On the one hand, we discuss the concentration of the bootstrap empirical…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…