Related papers: On the mean projection theorem for determinantal p…
We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes. The latter have applications to…
We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some…
Hierarchical inductive biases are hypothesized to promote generalizable policies in reinforcement learning, as demonstrated by explicit hyperbolic latent representations and architectures. Therefore, a more flexible approach is to have…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…
The Aldous diffusion is a conjectured Markov process on the space of real trees that is the continuum analogue of discrete Markov chains on binary trees. We construct this conjectured process via a consistent system of stationary evolutions…
The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.
We study the relation between sweeping processes with the cone of limiting normals and projection processes. We prove the existence of solution of a perturbed sweeping process with the cone of limiting normals and of nonstationary…
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…
For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…
Assume that a family of stochastic processes on some Polish space $E$ converges to a deterministic process; the convergence is in distribution (hence in probability) at every fixed point in time. This assumption holds for a large family of…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
In this paper we study the exponential decay of posterior probability of a set of sources and conditioning by rare sources for both uniform and general prior distributions of sources. The decay rate is determined by $L$-divergence and rare…
We prove that for a discrete determinantal process the BK inequality occurs for increasing events generated by simple points. We give also some elementary, but nonetheless appealing relationship, between a discrete determinantal process and…
The aim of this paper is threefold. Firstly, we develop the author's previous work on the dynamical relationship between determinantal point processes and CAR algebras. Secondly, we present a novel application of the theory of stochastic…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…
This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length…