TY - INPR A1 - Zessin, Hans T1 - Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010 N2 - The aim of these lectures is a reformulation and generalization of the fundamental investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 06 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49619 ER - TY - INPR A1 - Nehring, Benjamin A1 - Zessin, Hans T1 - A path integral representation of the moment measures of the general ideal Bose gas N2 - We reconsider the fundamental work of Fichtner ([2]) and exhibit the permanental structure of the ideal Bose gas again, using another approach which combines a characterization of infinitely divisible random measures (due to Kerstan,Kummer and Matthes [5, 6] and Mecke [8, 9]) with a decomposition of the moment measures into its factorial measures due to Krickeberg [4]. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain path integrals. This representation can be considered as a point process analogue of the old idea of Symanzik [11] that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing the one of the classical ideal Bose gas considered by Fichtner. It is well known that the calculation of moments of higher order of point processes are notoriously complicated. See for instance Krickeberg's calculations for the Poisson or the Cox process in [4]. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 10 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49635 ER - TY - INPR A1 - Nehring, Benjamin A1 - Poghosyan, Suren A1 - Zessin, Hans T1 - On the construction of point processes in statistical mechanics N2 - By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 5 KW - Levy measure KW - cluster expansion KW - Gibbs perturbation KW - DLR equation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64080 ER - TY - JOUR A1 - Poghosyan, Suren A1 - Zessin, Hans T1 - Construction of limiting Gibbs processes and the uniqueness of Gibbs processes JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472015 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 55 EP - 64 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Zass, Alexander A1 - Zagrebnov, Valentin A1 - Sukiasyan, Hayk A1 - Melkonyan, Tatev A1 - Rafler, Mathias A1 - Poghosyan, Suren A1 - Zessin, Hans A1 - Piatnitski, Andrey A1 - Zhizhina, Elena A1 - Pechersky, Eugeny A1 - Pirogov, Sergei A1 - Yambartsev, Anatoly A1 - Mazzonetto, Sara A1 - Lykov, Alexander A1 - Malyshev, Vadim A1 - Khachatryan, Linda A1 - Nahapetian, Boris A1 - Jursenas, Rytis A1 - Jansen, Sabine A1 - Tsagkarogiannis, Dimitrios A1 - Kuna, Tobias A1 - Kolesnikov, Leonid A1 - Hryniv, Ostap A1 - Wallace, Clare A1 - Houdebert, Pierre A1 - Figari, Rodolfo A1 - Teta, Alessandro A1 - Boldrighini, Carlo A1 - Frigio, Sandro A1 - Maponi, Pierluigi A1 - Pellegrinotti, Alessandro A1 - Sinai, Yakov G. ED - Roelly, Sylvie ED - Rafler, Mathias ED - Poghosyan, Suren T1 - Proceedings of the XI international conference stochastic and analytic methods in mathematical physics N2 - The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here. T3 - Lectures in pure and applied mathematics - 6 KW - statistical mechanics KW - random point processes KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-459192 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER -