Related papers: Descent-Inversion Statistics in Riffle Shuffles
We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\pi \in \mathbb{S}_n$ is proportional to $q^{\textrm{inv}(\pi)}$ where $0<q\le 1$ and…
Statistical properties of circulation encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, as the dependence of circulation…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of…
We study numerically the distributions of the length $L$ of the longest increasing subsequence (LIS) for the two cases of random permutations and of one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able…
Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical stability results for deterministic and random perturbations in these kind of…
This paper presents results of a theoretical investigation of transport in a numerical model of a two-dimensional Kolmogorov flow. We investigate the changes in its mixing properties associated with transition from laminar regime to…
The goal of this paper is to go further in the analysis of the behavior of the number of descents in a random permutation. Via two different approaches relying on a suitable martingale decomposition or on the Irwin-Hall distribution, we…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
A ballot permutation is a permutation $\pi$ such that in any prefix of $\pi$ the descent number is not more than the ascent number. By using a reversal concatenation map, we give a formula for the joint distribution (pk, des) of the peak…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
The exit time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (Inverse Structure Functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
Finding distributions of permutation statistics over pattern-avoiding classes of permutations attracted much attention in the literature. In particular, Bukata et al. found distributions of ascents and descents on permutations avoiding any…
This paper provides a quantitative version of de Finetti law of large numbers. Given an infinite sequence $\{X_n\}_{n \geq 1}$ of exchangeable Bernoulli variables, it is well-known that $\frac{1}{n} \sum_{i = 1}^n X_i…