相关论文: The maximum deviation of the Sine$_\beta$ counting…

In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…

In recent work, Fyodorov and Keating conjectured the maximum size of $|\zeta(1/2+it)|$ in a typical interval of length O(1) on the critical line. They did this by modelling the zeta function by the characteristic polynomial of a random…

This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…

We find the precise rate at which the empirical measure associated to a $\beta$-ensemble converges to its limiting measure. In our setting the $\beta$-ensemble is a random point process on a compact complex manifolds distributed according…

We study the correlations of the celebrated Sine$_\beta$ point process. This point process arises as the bulk scaling limit of $\beta$-ensembles and has a geometric description through the Brownian carousel, as shown by Valk\'o and Vir\'ag…

We consider the asymptotic behavior of the expectation of the maximum for a special assignment process with constant or i.i.d. coefficients. We show how it depends on the coefficients' distribution.

The goal of this paper is to characterize Gaussian-Process optimization in the setting where the function domain is large relative to the number of admissible function evaluations, i.e., where it is impossible to find the global optimum. We…

Motivated by recent works on the high-dimensional logistic regression, we establish that the existence of the maximum likelihood estimate exhibits a phase transition for a wide range of generalized linear models with binary outcome and…

Our work is devoted to the study of Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's $G$-expectation. The dynamics of the controlled state process is given by a stochastic differential equation…

Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…

We study the total mass of high points in a random model for the Riemann-Zeta function. We consider the same model as in [8], [2], and build on the convergence to 'Gaussian' multiplicative chaos proved in [14]. We show that the total mass…

We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to…

We consider the problem of sequential hypothesis testing by betting. For a general class of composite testing problems -- which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of…

This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that…

The beta distribution serves as a canonical tool for modeling probabilities in statistics and machine learning. However, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent…

We explore the behavior and establish new properties of the cumulative-sum process (CUSUM) and its running maximum. The study includes precise expressions for CUSUM's moment generating function and moments, fast recursive computing…

We describe the behavior of the expectation of the maximum for a random assignment process built upon a square matrix with independent entries. Under mild assumptions on the underlying distribution, the answer is expressed in terms of its…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

Stochastic process discovery is concerned with deriving a model capable of reproducing the stochastic character of observed executions of a given process, stored in a log. This leads to an optimisation problem in which the model's parameter…

We extend Peng's maximum principle to the case of stochastic delay differential equations of mean-field type. More precisely, the coefficients of our control problem depend on the state, on the past trajectory and on its expected value.…