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Runtime monitoring/verification is a lightweight technique that complements other verification methods in a multi-pronged approach towards ensuring software correctness. The technique poses novel questions to software engineers: it is not easy to see which specifications are amenable to runtime monitoring, and it is not clear which monitors perform the required ...
Bordenave and Caputo (2014) defined a notion of entropy for probability distributions on rooted graphs with finite expected degree at the root. When such a probability distribution \rho has finite BC entropy \Sigma(\rho), the growth in the number of vertices n of the number of graphs on n vertices whose ...
We will discuss a couple of results and questions regarding the structure of large graphs. These include vertex transitive graphs, expanders and random graphs.
The theme of this talk is the sampling of cluster and iterated cluster point processes. It is partially a review, mainly of the Brix–Kendall exact sampling method for cluster point processes and its adaptation by Moller and Rasmussen to Hawkes branching point processes on the real line with light-tail fertility ...
A Poisson outdegree-one graph is a directed graph based on a marked Poisson point process such that each vertex has only one outgoing edge. We state the absence of percolation for such graphs satisfying two assumptions. The Shield assumption roughly says that the graph is locally determined with possible random ...
Random planar maps have been the subject of numerous studies over the last years. They are instance of stationary and reversible random planar maps exhibiting a non-conventional geometry at large scale. Because of their “fractal” geometry, the simple random walk on these random graphs is believed to be subdiffusive, i.e. ...
The notion of discrete alpha-stable point processes generalizes to point processes the notion of stable distribution. It has been introduced and studied by Davydov, Molchanov and Zuyev a few years ago. Their stability property leaves a large degree of variability in the choice of their driving characteristics but enforces a ...
We shall consider Euclidean stationary point processes which have fast decay of correlations i.e., their correlation functions factorize upto an additive error decaying exponentially in the separation distance. By a quasi-local statistic of the point process, we refer to statistics that can be expressed as sum of contributions from the ...
This talk is centered on covariant dynamics on unimodular random graphs and random networks (marked graphs), namely maps from the set of vertices to itself which are preserved by graph or network isomorphisms. Such dynamics are referred to as vertex-shifts here. These dynamics have point-shifts on point processes as a ...
In this talk we will define notions of dimension for unimodular random graphs and point-stationary point processes. These notions are in spirit similar to the Minkowski dimension and the Hausdorff dimension. The key point in the definitions is the use of the mass transport principle which is used indispensably and ...
 
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