Quasi-Flows II Additive Functionals and TQ-Systems

Scaling Limits of Additive Functionals of Interacting Particle Systems

Using the renormalization method introduced in [17], we prove what we call the local Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension d = 1. As applications of this result, we obtain various scaling limits of additive functionals of particle systems, like the occupation time of a given site or extensive additive fields of the dynamics. As a by-pro...

Rates of Convergence for Quasi-Additive Smooth Euclidean Functionals and Application to Combinatorial Optimization Problems

Rates of convergence of limit theorems are established for a class of random processes called here quasi-additive smooth Euclidean functionals. Examples include the objective functions of the traveling salesman problem, the Steiner tree problem, the minimumspanning tree problem, the minimumweight matching problem, and a variant of the minimum spanning tree problem with power weighted edges.

Representation of additive and biadditive functionals

Additive functionals and excursions of Kuznetsov processes

Let B be a continuous additive functional for a standard process (Xt)t∈R+ and let (Yt)t∈R be a stationary Kuznetsov process with the same semigroup of transition. In this paper, we give the excursion laws of (Xt)t∈R+ conditioned on the strict past and future without duality hypothesis. We study excursions of a general regenerative system and of a regenerative system consisting of the closure of...

Additive functionals on multiway search trees

We derive asymptotics of moments and limiting distributions, under the random permutation model on m-ary search trees on n keys, of functionals that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal path length, and the socalled shape functional fall under this framework. The limiting behavior of these functionals exhibi...