Advanced Courses

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Course on Spatial Stochastic Processes

The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this summer school is to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory: Stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis.

Courses  The following sets of 5/6 hours lectures each in English will be offered:

• Mixing results for Critical Nearest Particle Systems via Spectral Gap Estimates, by Tom Mountford (University of California, Los Angeles)
• Level sets and excursions of the Brownian sheet, by Robert Dalang (Ecole Polytechnique Fédérale de Lausanne)
• Weak convergence of set-indexed martingales, by Gail Ivanoff (University of Ottawa)
• Set-indexed martingales and point processes, by Ely Merzbach (Bar-Ilan University)
• Stochastic Geometry of spatially structured birth and growth processes with applications to polymers crystallization processes, by Vincenzo Capasso (Universitŕ di Milano)
• Local time and sample path properties of n-parameter processes, by Marc Dozzi (University of Nancy)

Seminars  A number of seminars will be offered during the course.

Lecture Notes These will be available as draft at the Course and will appear soon after in the CIME subSeries of the Springer-Verlag Lecture Notes in Mathematics.

Applications  Contact CIME via the above-indicated Web page. No registration fees are due.

An important consideration in the acceptance of the application is the scientific relevance of the Course to the field of interest of the applicant. Applicants are requested therefore to submit along with their application, a scientific curriculum and a letter of recommendation.

There is a chance of having your expenses partially covered by the European Union. The action of the programme is intended to support young scientists up to 35 years old. Researchers should be citizen of a member state of the European Union or reside in such a state for at least one year. Please quote in the application the need of support and conditions for eligibility.

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