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- Polymer measure: varadhan's renormalization revisitedPublication . Bock, Wolfgang; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigThrough chaos decomposition we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.
- Stochastic and infinite dimensional analysisPublication . Bernido, Christopher C.; Carpio-Bernido, Maria Victoria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria João; Silva, José Luís daThis volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
- Intersection local times of fractional Brownian motions with H∈(0,1) as generalized white noise functionalsPublication . Drumond, Custódia; Oliveira, Maria João; Silva, José Luís daIn R^d, for any dimension d ≥ 1, expansions of self-intersection local times of fractional Brownian motions with arbitrary Hurst coefficients in (0,1) are presented. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals.
- Self-avoiding fractional Brownian motion: the Edwards modelPublication . Grothaus, Martin; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigIn this work we extend Varadhan’s construction of the Edwards polymer model to the case of fractional Brownian motions in Rd , for any dimension d ≥ 2, with arbitrary Hurst parameters H ≤ 1/d.
- Results about the free kawasaki dynamics of continuous particle systems in infinite volume: long-time asymptotics and hydrodynamic limitPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigAn infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled, further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second quantization are discussed. The hydrodynamic limit for a general initial distribution satisfying a mixing condition is derived. The long-time asymptotics is computed under an extra assumption. The relation with constructions based on infinite volume limits is discussed.
- Studies in fractional poisson measuresPublication . Silva, José Luís da; Oliveira, Maria JoãoIn this paper we investigate the quasi-invariance property of fractional Poisson measures with respect to the diffeomorphism subgroup and we construct spaces of test and generalized functions associated to the corresponding fractional Lebesgue-Poisson measures.
- Intersection local times of independent fractional Brownian motions as generalized white noise functionalsPublication . Oliveira, Maria João; Silva, José Luís da; Streit, LudwigIn this work we present expansions of intersection local times of fractional Brownian motions in R^d , for any dimension d ≥ 1, with arbitrary Hurst coefficients in (0, 1)^d . The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals. As an application of our approach, a sufficient condition on d for the existence of intersection local times in L^2 is derived, extending the results in Nualart and Ortiz-Latorre (J. Theoret. Probab. 20(4):759–767, 2007) to different and more general Hurst coefficients.