TY  - BOOK
A1  - Dereudre, David
A1  - Roelly, Sylvie
T1  - On Gibbsianness of infinite-dimensional diffusions
N2  - We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice $Z^{d} : X = (X_{i}(t), i ∈ Z^{d}, t ∈ [0, T], 0 < T < +∞)$. In a first part, these processes are characterized as Gibbs states on path spaces of the form $C([0, T],R)Z^{d}$. In a second part, we study the Gibbsian character on $R^{Z}^{d}$ of $v^{t}$, the law at time t of the infinite-dimensional diffusion X(t), when the initial law $v = v^{0}$ is Gibbsian.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 01 
KW  - infinite-dimensional Brownian diffusion
KW  - Gibbs field
KW  - cluster expansion
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-52630
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  - INPR
A1  - Roelly, Sylvie
A1  - Ruszel, Wioletta M.
T1  - Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction
N2  - We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)18 
KW  - infinite-dimensional diffusion
KW  - cluster expansion
KW  - non-Markov drift
KW  - Girsanov formula
KW  - ultracontractivity
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-69014
ER  -