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Nombre de programmes trouvés : 39
Conférences

le (42m40s)

Stein-Malliavin method for discrete alpha stable point processes (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

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 rich mathematical structure. We show how to build a Dirichlet-Malliavin structure for these processes and we apply this framework to several limit theorems. Some known results for Poisson point processes appear as corollaries of ...
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Conférences

le (50m57s)

Point processes, cost and the growth of rank for locally compact groups (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

The cost of a vertex transitive graph is the infimum of the expected degree of an invariant random wiring of the graph. Similarly, one can define the cost of a point process on a homogeneous space, as the infimum of the average degree of a factor wiring on its points. It turns out that the cost of a Poisson process is maximal among point processes of the same density, by proving that all free processes weakly contain the Poisson. The cost is related to the growth ...
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Conférences

le (39m53s)

Emergence of extended states at zero in the spectrum of sparse random graphs (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

We confirm the long-standing prediction that c=e≈2.718 is the threshold for the emergence of a non-vanishing absolutely continuous part (extended states) at zero in the limiting spectrum of the Erdős-Renyi random graph with average degree c. This is achieved by a detailed second-order analysis of the resolvent (A−z)−1 near the singular point z=0, where A is the adjacency operator of the Poisson-Galton-Watson tree with mean offspring c. More generally, our method applies to arbitrary unimodular Galton-Watson trees, yielding explicit criteria for the presence or ...
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Conférences

le (55m56s)

A notion of entropy for limits of sparse marked graphs (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

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 associated rooted graph distribution is close to \rho is as d/2 n \log n + \Sigma(\rho) n + o(n), where d is expected degree of the root under \rho. We develop the parallel result for probability distributions on marked rooted graphs. Our graphs have vertex marks drawn from a finite ...
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Conférences

le (53m51s)

Subdiffusivity of random walks on random planar maps, via stationarity (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

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. it displaces slowler than in the regular grid case. We will propose an approach to such results strongly based on the stationary of these random graphs, i.e. the fact that their distributions is invariant under ...
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Conférences

le (46m11s)

Central Limit theorem for quasi-local statistics of point processes with fast decay of correlations (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

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 points and the contribution of every point being determined by a random ball around the point whose radius has an exponential tail. There are many well-known point processes and statistics that satisfy these conditions ...
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Colloques

le (31m29s)

évolution, répartition et gestion des réseaux d’évacuation des eaux usées dans le quartier urbain antique de Saint-Romain-en-Gal (Ier s. av. J.-C. – IIe s. ap. J.-C.)

... (Brissaud, 2006). Jaugé à l’aune du plan du dernier état du quartier, ce réseau d’évacuation des eaux usées qui révèle un collecteur par rue, peut paraître simple et homogène. Pourtant, cette apparente cohérence masque le long et progressif processus de...
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