相关论文: Obstructions to uniformity, and arithmetic pattern…
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
The concept of impedance, which characterises the current response to a periodical driving, is introduced in the context of stochastic transport. In particular, we calculate the impedance for an exactly solvable model, namely the stochastic…
The idea of a parsing of a stationary process according to a collection of words is introduced, and the basic framework required for the asymptotic analysis of these parsings is presented. We demonstrate how the pointwise ergodic theorem…
The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical…
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…
When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…
This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The…
One of the questions of distribution of prime numbers is considered in the article. It is shown what error is obtained from the assumption that the asymptotic density of a sequence of primes is a probability. Various forms of an analogue of…
We prove the uniform oscillation and jump inequalities for the polynomial ergodic averages modeled over multi-dimensional subset of primes. These inequalities provide endpoints for the $r$-variational estimates obtained by Trojan…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
We study the following problem: Is it possible to explain the quantum interference of probabilities in the purely corpuscular model for elementary particles? We demonstrate that (by taking into account perturbation effects of measurement…
We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
We study perturbation theory and uniform ergodicity for discrete-time Markov chains on general state spaces in terms of the uniform moments of the first hitting times on some set. The methods we adopt are different from previous ones. For…
The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…
The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability…
We discuss some regularity issues in the study of the obstacle problem. In particular, we present a recent result by O. Savin and the author on the regularity of the singular set for the obstacle problem with a fully nonlinear elliptic…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.