{"250021":{"#nid":"250021","#data":{"type":"event","title":"ARC Colloquium: Francois Baccelli, The University of Texas at Austin","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETitle:\u003C\/strong\u003E Geometric Routing in Stochastic Networks, Point-Shift and Palm Probabilities of a Point Process\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EAbstract: \u003C\/strong\u003EConsider a point process in the Euclidean space and a rule defining the edges that exist between its points. This defines a random graph on the point process. A routing algorithm constructs, for all pairs of points, a route between these points, namely a path of this graph connecting them, when possible. Such an algorithm can be global, like in shortest path routing, or local, like in geographic or geometric routing.\u003C\/p\u003E\u003Cp\u003EThis talk will discuss properties of routes which are locally defined on a stationary point process, using the notion of point-shift.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;A point-shift maps, in a translation invariant way, each point of a stationary point process Z to some point of Z. The existence of stationary regimes of a routing algorithm is then equivalent to that of probability measures, defined on the space of counting measures with an atom at the origin, which are left invariant by the point-shift f describing the local algorithm. The point-shift probabilities of Z are defined from the action of the semigroup of point-shift translations on the space of Palm probabilities, and more precisely from the compactification of the orbits of this semigroup action. If the point-shift probability is uniquely defined, and if f is continuous with respect to the vague topology, then the point-shift probability of Z provides a solution to the stationary regime question.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;Point-shift probabilities are shown to be a strict generalization of Palm probabilities: when the considered point-shift f is bijective, the point-shift-probability of Z boils down to the Palm probability of Z. When it is not bijective, there exist cases where the point-shift-probability of Z is the law of Z under the Palm probability of some stationary thinning Y of Z. But there also exist cases where the point-shift-probability of Z is singular w.r.t. the Palm probability of Z and where, in addition, it cannot be the law of Z under the Palm probability of any stationary point process Y jointly stationary with Z. The talk will give a criterion for the existence of point-shift probabilities of a stationary point process and will discuss uniqueness. The results will be illustrated through several examples.\u003C\/p\u003E\u003Cp\u003EJoint work with Mir-Omid Haji-Mirsadeghi, Sharif University, Department of Mathematics.\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":"","uid":"27263","created_gmt":"2013-10-31 10:04:32","changed_gmt":"2016-10-08 02:05:30","author":"Elizabeth Ndongi","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2013-11-08T15:00:00-05:00","event_time_end":"2013-11-08T15:00:00-05:00","event_time_end_last":"2013-11-08T15:00:00-05:00","gmt_time_start":"2013-11-08 20:00:00","gmt_time_end":"2013-11-08 20:00:00","gmt_time_end_last":"2013-11-08 20:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"70263","name":"ARC"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003E\u003Ca href=\u0022mailto:ndongi@cc.gatech.edu\u0022\u003Endongi@cc.gatech.edu\u003C\/a\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}