### A class of nonstationary adic transformations

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One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...

The main purpose of this paper is to analyze a development of a scenario suggested by Baston and Garnaev (2005) for modelling the situation where two departments in a large organization are each seeking to make an appointment within the same area of expertise, for instance, a computer science specialist. The departments are interested in three skills of the candidate (say, writing code, communication and in algorithms). In our scenario Department 1 wants to employ a candidate with excellent skills...

We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...

We show that the family of all lines in the plane which is a VC class of index 2 cannot be obtained in a finite number of steps starting with VC classes of index 1 and applying the operations of intersection and union. This confirms a common belief among specialists and solves a question asked by several authors.

We present a random automorphism-invariant subgraph of a Cayley graph such that with probability 1 its exponential growth rate does not exist.