In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance D(x, y) between two points is the length of the shortest open path between these two points. Thus, we study the size of random fluctuations around the mean value, and also the asymptotic behavior of this mean value. The estimates we obtain improve our knowledge of the conver...

It is known that the transport capacity of a dense wireless ad hoc network with n nodes scales like √ n. We show that the transport capacity divided by √ n approaches a non-random limit with probability one when the nodes are i.i.d uniformly distributed on the unit square. To show the existence of the limit we prove that the transport capacity under the protocol model is a subadditive Euclidean...

We study hierarchical properties of Sturmian words. These properties are similar to those of substitution dynamical systems. This approach allows one to carry over to Sturmian dynamical systems methods developed in the context of substitutions. For example, it allows for a proof of an ergodic type theorem for additive functions taking values in a Banach space. We then focus on establishing vari...

Process complexity is one of the basic variants of Kolmogorov complexity. Unlike plain Kolmogorov complexity, process complexity provides a simple characterization of randomness for real numbers in terms of initial segment complexity. Process complexity was first developed in [11]. Schnorr’s definition of a process, while simple, can be difficult to work with. In many situations, a preferable d...

Complexity results are obtained with regard to problems of finding solutions to set of linear inequalities which are compatible with some set-functions and a prescribed intersection graph. It is shown that the additive case is SP-complete, the superadditive case is coSP-complete, and the subadditive case is in P. 0 1 1 Finding Addit,ive, Superaddit.ive and Subadditive Set-Functions Subject to L...

We study the Price of Anarchy of simultaneous first-price auctions for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian Price of Anarchy of these auctions are e/(e− 1) [Syrgkanis and Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching lower bounds for both cases even for the case of full information and for mixed Nash equi...

In this paper, we lay the foundation for the study of the two-dimensional mixed integer infinite group problem (2DMIIGP). We introduce tools to determine if a given continuous and piecewise linear function over the two-dimensional infinite group is subadditive and to determine whether it defines a facet. We then present two different constructions that yield the first known families of facet-de...

Abstract A central property of a classical geometry is that the geodesic distance between two events additive. When considering quantum fluctuations in metric or statistical superposition different spacetimes, additivity generically lost at level expectation values. In presence metrics, distances can be made diffeomorphism invariant by frame family free-falling observers pressureless fluid, pro...