Related papers: Polynomial escape rates via maximal large deviatio…
We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
We consider large-scale Markov decision processes (MDPs) with a risk measure of variability in cost, under the risk-aware MDPs paradigm. Previous studies showed that risk-aware MDPs, based on a minimax approach to handling risk, can be…
It is well known that open dynamical systems can admit an uncountable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based…
We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a…
We show that dynamical systems with $\phi$-mixing measures have local escape rates which are exponential with rate $1$ at non-periodic points and equal to the extremal index at periodic points. We apply this result to equilibrium states on…
The Polyhedral Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function $f: \mathbb{R}^{d} \rightarrow \mathbb{R}^{d}$ and a convex polyhedron $\mathcal{P} \subseteq \mathbb{R}^{d}$, whether, for…
We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set which can be thought of as a small hole. The presence of the latter influences the extremal index…
Escape rate in the low-to-intermediate damping connecting the low damping with the intermediate damping is established for the power-law distribution on the basis of flux over population theory. We extend the escape rate in the low damping…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
We consider random walks on the set of all words over a finite alphabet such that in each step only the last two letters of the current word may be modified and only one letter may be adjoined or deleted. We assume that the transition…
Computer experiments are pivotal for modeling complex real-world systems. Maximizing information extraction and ensuring accurate surrogate modeling necessitates space-filling designs, where design points extensively cover the input domain.…
We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…
In this paper, building on previous work, we extend the thermodynamic formalism for random open dynamical systems generated by piecewise monotone interval maps with countably many branches. Under summable and contracting assumptions on the…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with…
The narrow escape problem consists of deriving the asymptotic expansion of the solution of a drift-diffusion equation with the Dirichlet boundary condition on a small absorbing part of the boundary and the Neumann boundary condition on the…
We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…
Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large…