Research
Research
Research
Research
13,626+ open-access research outputs.
We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) da…
We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly …
We study the effective estimation of the diffusivity and Hurst parameter for the homogenized limit of a class of slow/fast systems. Depending on the system parameters, this limit solves a stochastic d…
Upon the introduction of the Metropolis algorithm, the question of how many steps in the Markov chain were needed to achieve convergence to stationarity became apparent. The convergence was rather slo…
We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing wit…
We study statistical properties of random numerical semigroups of a given genus. We analyze the graph of a typical numerical semigroup, understood as a function from $\mathbb{N}$ to $\mathbb{N}$. If $…
Based on discrete observations $X_0,X_{\Delta},\dots, X_{n\Delta}$ for $\Delta=n^{-\gamma}$ with $\gamma\in [0,1)$ of the null-recurrent dynamic $dX_t = \sigma(X_t)dW_t$ with a Brownian motion $W$ and…
The continuous linear $P(k; N, w)$ and circular scan statistics $P_c(k; N, w)$ are fundamental tools in probability and spatial statistics, frequently used to detect clustering in uniform data. Let $X…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the li…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metr…
The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Bernoulli-Laplace mode…
Kac's walk on the rotation group, introduced by Hastings in 1970, is an important high-dimensional Markov chain with applications in statistical physics, statistics, cryptography, and computational sc…
This study aims to examine the historical air pollution data from major Indian cities using fractal analysis to measure environmental risk. The fractal dimension of the major air pollutants is compute…
We prove lower bounds on learning the M\"obius or Liouville function with a variety of standard learning techniques, including kernel methods, noisy gradient methods, and correlational statistical que…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion model…
We study the inverse optimal transport problem of recovering the ground cost from an optimal transport plan. In discrete settings, this problem reduces to inverse linear programming and is intrinsical…
We investigate barycenters of Gaussian process laws in adapted Wasserstein space. The adapted Wasserstein distance refines classical optimal transport by enforcing compatibility of transport plans wit…
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map …
Stochastic programming models for decision-making under uncertainty often suffer from scenario scarcity, where obtaining representative samples of uncertain parameters requires expensive simulations o…
This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their asso…
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