Related papers: Rare events for Cantor target sets
This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…
Rare events play a key role in many applications and numerous algorithms have been proposed for estimating the probability of a rare event. However, relatively little is known on how to quantify the sensitivity of the probability with…
We study rare event simulations of semimartingale reflecting Brownian motions (SRBMs) in an orthant. The rare event of interest is that a $d$-dimensional positive recurrent SRBM enters the set $B_n = \{z\in\mathbb{R}^d: \sum_{k=1}^d z_k =…
We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in…
We investigate the effect of weak gravitational lensing in the limit of small angular scales where projected galaxy clustering is strongly nonlinear. This is the regime likely to be probed by future weak lensing surveys. We use…
We consider the feasibility of directly observing gravitational microlensing in extra-galactic sources, whose stars are not generally resolved. This precludes use of the simple optical depth to microlensing formulation, which is applicable…
Extreme scattering events (ESEs) are distinctive fluctuations in the brightness of astronomical radio sources caused by occulting plasma lenses in the interstellar medium. The inferred plasma pressures of the lenses are $\sim 10^3$ times…
We characterize and phenomenologically model the merger-ringdown of gravitational waves emitted by a small compact object that plunges and merges into a Kerr black hole from equatorial-eccentric inspirals. The waveforms are generated…
We study the dynamics of a collection of nonlinearly coupled limit cycle oscillators, relevant to systems ranging from neuronal populations to electrical circuits, under coupling topologies varying from a regular ring to a random network.…
The Emergent String Conjecture constrains the possible types of light towers in infinite-distance limits in quantum gravity moduli spaces. In this paper, we use these constraints to restrict the geometry of the scalar charge-to-mass vectors…
The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and…
Extreme events (sometimes also called optical rogue waves), in the form of pulses of extraordinary intensity, are easily observed in its chaotic regime if the Fresnel number of the cavity is high. This result suggests that the nonlinear…
The thin string limit of Cosmic Strings is investigated using a description in terms of Colombeau's theory of nonlinear generalised functions. It is shown that in this description the energy-momentum tensor has a well defined thin string…
In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated…
We assess the detectability of the gravitational wave signals from highly eccentric compact binaries. We use a simple model for the inspiral, merger, and ringdown of these systems. The model is based on mapping the binary to an effective…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
We analyse extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one dimensional periodic potential. Based on more than 500…
Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…