Related papers: On a Very Steep Version of the Standard Map
This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the…
We devise an abstract, modular scheme to prove continuity of the Lyapunov exponents for a general class of linear cocycles. The main assumption is the availability of appropriate large deviation type (LDT) estimates which are uniform in the…
We give a complete classification of the set of parameters $\kappa$ for which the singular value of $E_{\kappa}:z\mapsto \exp(z)+\kappa$ escapes to infinity under iteration. In particular, we show that every path-connected component of this…
We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described.…
We look at degenerating meromorphic families of rational maps on $\mathbb{P}^1$ -- holomorphically parameterized by a punctured disk -- and we provide examples where the bifurcation current fails to have a bounded potential in a…
We consider the simple random walk on supercritical percolation clusters in the multidimensional cubic lattice. In this model, a quenched large deviation principle holds for the position of the random walk. Its rate function depends on the…
The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. We provide a polynomial-time algorithm to decide CPEP for…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for…
This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…
We study the continuity of many channel parameters and operations under various topologies on the space of equivalent discrete memoryless channels (DMC). We show that mutual information, channel capacity, Bhattacharyya parameter,…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
We prove that the limit profile of a sequence of reversible Markov chains exhibiting total variation cutoff is a continuous function, under a computable condition involving the spectrum of the transition matrix and the cutoff window.
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…
We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the…
By a theorem of Volkov (2001) we know that on most graphs with positive probability the linearly vertex-reinforced random walk (VRRW) stays within a finite "trapping" subgraph at all large times. The question of whether this tail behavior…
We present a novel path-integral method for the determination of time-dependent and time-averaged reaction rates in multidimensional, periodically driven escape problems at weak thermal noise. The so obtained general expressions are…
We prove a formula for the speed of distance stationary random sequences generalizing the law of large numbers of Karlsson and Ledrappier. A particular case is the classical formula for the largest Lyapunov exponent of i.i.d.\ matrix…
A classical approach for the analysis of the longtime behavior of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally $\Phi$-entropies. Via purely analytic arguments it can be shown that these…
We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general…