Related papers: Asymptotic sequential Rademacher complexity of a f…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
A rigorous study is carried out for the randomly forced Burgers equation in the inviscid limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of…
We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal…
This work is devoted to solving some closely related open problems on the average and asymptotic behavior of the $2$-adic complexity of binary sequences. First, for fixed $N$, we prove that the expected value $E^{\mathrm{2-adic}}_N$ of the…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the…
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the winding number as the time horizon tends to infinity.…
We study expected values of the polynomials $P_N^{}(z)=\prod_{1\leq n\leq N}(X_n^2+z^2)$ whose $2N$ zeros $\{\pm i X_k\}^{}_{k=1,...,N}$ are generated by $N$ identically distributed multi-variate mean-zero normal random variables…
The asymptotics, as $n\to\infty$, for the expected number of distinct part sizes in a random composition of an integer n is obtained.
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant $\delta$. The bound is expressed in the uniform entropy integral of…
This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the…
Current performance bounds for randomized iterative methods are often considered tight under per-iteration analyses, yet they are notoriously loose in practice. We derive asymptotic performance bounds that narrow this theory-practice gap,…
We provide non-asymptotic bounds for first and higher order inclusion probabilities of the rejective sampling model with various size parameters. Further we derive bounds in the semi-definite ordering for matrices that collect (conditional)…
We introduce the notion of a random matrix-valued multiplicative function, generalizing Rademacher random multiplicative functions to matrices. We provide an asymptotic for the second moment based on a linear recurrence property for…
Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.