Realizability problems with regularity conditions: Applications to point processes and random closed sets

Raphael Lachieze - Rey

Description

Realizability problems with regularity conditions: Applications to point processes and random closed sets Raphael Lachieze-Rey, Luxembourg University, Joint work with Ilya Molchanov, Bern University Workshop on Geometry and Physics of Spatial Random Systems, Bad Herrenalb Raphael Lachieze-Rey () Realizability problems with regularity conditions: Applications to point processes and random closed sets1 / 28

• point processes


• random closed


• given only


• semi-definite positive


• px


• small numeric


• spatial random

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 29
• Langue: English

Extrait

Realizabilityproblemswithregularityconditions: Applicationstopointprocessesandrandomclosedsets R Raphae¨lLachie`ze-Rey,LuxembourgUniversity, JointworkwithIlyaMolchanov,BernUniversity WorkshoponGeometryandPhysicsofSpatialRandomSystems, BadHerrenalb paahle¨aLcihze`-eeRy)(eRlazibalitiyrpboelsmiwhterugalirytocdntioisn:pAlpcitaoisnotpiotnrpoecsssena1d/ra2n8domlcoesdstes

1 2 3 Introductiontotherealisabilityproblemsinstochasticgeometry Thecompactcase Regularitymodulus aRhpe¨alaLcihze`-eeRy)(eRlazibalitiyrpboelsmiwhterugalirytocdntioisn:pApilacitnosotpiotnrpoecsssena2d/ra2n8domlcoesdstes

Randomclosedsets R X:Polishspace. F :lCsodeesstfoX. T :Fell’stopologyon F ( ∼ aRdnmolcsoedes:taRdn H o a m u e s l d e P ro m ff en m t e F t 1-pointcoveringfunction:p x =(x ∈ F). ir o c f fiXoc ( F , T ). pmca)t. mredrots1“”lanigra Covariancefunction:p x,y = P (x,y ∈ F).“2dordermarginal” paahle¨aLcihze`-eeRy)(eRlazibalitiyrpboelsmiwhterugalirytocdntioisn:pAlpcitaoisnotpiotnrpoecsssena3d/ra2n8domlcoesdstes