arXiv subjects
Publications and source records attributed to Ludwig Streit.
We extend Varadhan's construction of the Edwards polymer model to fractional Brownian loops and fractional Brownian starbursts. We show that, as in the fBm case, the Edwards density under a renormalizaion is an integrable function for the case H<= 1/d.
Various authors have invoked discretized fractional Brownian (fBm) motion as a model for chain polymers with long range interaction of monomers along the chain. We show that for these, in contrast to the Brownian case, linear forces are acting between all pairs of constituents, attractive for small Hurst index H and mostly repulsive when H is larger than 1/2. In the second part of this paper we extend this study to periodic fBm and related models with a view to ring polymers with long range interactions.
In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain a closed analytic expressions for the form factors, the Debye functions and their asymptotic decay. The relation between the end-to-halftime and radius of gyration is computed for these classes of periodic processes.
For certain Sheffer sequences $(s_n)_{n=0}^\infty$ on $\mathbb C$, Grabiner (1988) proved that, for each $α\in[0,1]$, the corresponding Sheffer operator $z^n\mapsto s_n(z)$ extends to a linear self-homeomorphism of $\mathcal E^α_{\mathrm{min}}(\mathbb C)$, the Fréchet topological space of entire functions of order at most $α$ and minimal type (when the order is equal to $α>0$). In particular, every function $f\in \mathcal E^α_{\mathrm{min}}(\mathbb C)$ admits a unique decomposition $f(z)=\sum_{n=0}^\infty c_n s_n(z)$, and the series converges in the topology of $\mathcal E^α_{\mathrm{min}}(\mathbb C)$. Within the context of a complex nuclear space $Φ$ and its dual space $Φ'$, in this work we generalize Grabiner's result to the case of Sheffer operators corresponding to Sheffer sequences on $Φ'$. In particular, for $Φ=Φ'=\mathbb C^n$ with $n\ge2$, we obtain the multivariate extension of Grabiner's theorem. Furthermore, for an Appell sequence on a general co-nuclear space $Φ'$, we find a sufficient condition for the corresponding Sheffer operator to extend to a linear self-homeomorphism of $\mathcal E^α_{\mathrm{min}}(Φ')$ when $α>1$. The latter result is new even in the one-dimensional case.
In this paper we construct a Markov process which has as invariant measure the fractional Edwards measure based on a $d$-dimensional fractional Brownian motion, with Hurst index $H$ in the case of $Hd=1$. We use the theory of classical Dirichlet forms. However since the corresponding self-intersection local time of fractional Brownian motion is not Meyer-Watanabe differentiable in this case, we show the closability of the form via quasi translation invariance of the fractional Edwards measure along shifts in the corresponding fractional Cameron-Martin space.
In this paper we investigate the energy functions for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. We obtain closed analytic form for the energy function, in particular we recover the Brownian and fractional Brownian motion cases.
In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.
We prove the existence of a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion in dimension $d\in\mathbb{N}$ with Hurst parameter $H\in(0,1)$ fulfilling $dH < 1$. The diffusion is constructed via Dirichlet form techniques in infinite dimensional (Gaussian) analysis. Moreover, we show that the process is invariant under time translations.
We study the chaos decomposition of self-intersection local times and their regularization, with a particular view towards Varadhan's renormalization for the planar Edwards model.
We use an off-lattice discretization of fractional Brownian motion and a Metropolis Algorithm to determine the asymptotic scaling of this discretized fractional Brownian motion under the influence of an excluded volume as in the Edwards and Domb-Joyce models. We find a good agreement between the Flory index describing the scaling of end-to-end length with a mean field formula proposed earlier for this class of models.
Paper is withdrawn due to further studies.
Through chaos decomposition we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.
We present an extension of the Edwards model for conformations of individual chain molecules in solvents in terms of fractional Brownian motion, and discuss the excluded volume effect on the end-to-end length of such trajectories or molecules.
In this work we extend Varadhan's construction of the Edwards polymer model to the case of fractional Brownian motions in $\R^d$, for any dimension $d\geq 2$, with arbitrary Hurst parameters $H\leq 1/d$.
Networks are a natural and popular mechanism for the representation and investigation of a broad class of systems. But extracting information from a network can present significant challenges. We present NetzCope, a software application for the display and analysis of networks. Its key features include the visualization of networks in two or three dimensions, the organization of vertices to reveal structural similarity, and the detection and visualization of network communities by modularity maximization.
We investigate research and development collaborations under the EU Framework Programs (FPs) for Research and Technological Development. The collaborations in the FPs give rise to bipartite networks, with edges existing between projects and the organizations taking part in them. A version of the modularity measure, adapted to bipartite networks, is presented. Communities are found so as to maximize the bipartite modularity. Projects in the resulting communities are shown to be topically differentiated.
In this work we present expansions of intersection local times of fractional Brownian motions in $\R^d$, for any dimension $d\geq 1$, 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 of D. Nualart and S. Ortiz-Latorre in "Intersection Local Time for Two Independent Fractional Brownian Motions" (J. Theoret. Probab.,20(4)(2007), 759-767) to different and more general Hurst coefficients.
An 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 asymptotic is computed under an extra assumption. The relation with constructions based on infinite volume limits is discussed.