Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling

By using the mirror coupling for solutions of SDEs driven by pure jump L\'evy processes, we extend some transportation and concentration inequalities, which were previously known only in the case where the coefficients in the equation satisfy a global dissipativity condition. Furthermore, by using the mirror coupling for the jump part and the coupling by reflection for the Brownian part, we extend analogous results for jump diffusions. To this end, we improve some previous results concerning such couplings and show how to combine the jump and the Brownian case. As a crucial step in our proof, we develop a novel method of bounding Malliavin derivatives of solutions of SDEs with both jump and Gaussian noise, which involves the coupling technique and which might be of independent interest. The bounds we obtain are new even in the case of diffusions without jumps.Comment: 40 pages, revised version, accepted for publication in Annales de l'Institut Henri Poincar\'e Probabilit\'es et Statistiques. The final manuscript is available at Project Euclid via https://projecteuclid.org/euclid.aihp/157320362

Coupling and exponential ergodicity for stochastic differential equations driven by L\'{e}vy processes

We present a novel idea for a coupling of solutions of stochastic differential equations driven by L\'{e}vy noise, inspired by some results from the optimal transportation theory. Then we use this coupling to obtain exponential contractivity of the semigroups associated with these solutions with respect to an appropriately chosen Kantorovich distance. As a corollary, we obtain exponential convergence rates in the total variation and standard $L^1$-Wasserstein distances.Comment: 40 pages, revised version, accepted for publication in Stochastic Processes and their Applications. The final manuscript is available at Elsevier via https://doi.org/10.1016/j.spa.2017.03.02

Equation of state for agents on graphs

Choice models for populations of agents on graphs are studied in terms of statistical thermodynamics. Equations of state are derived and discussed for different connectivity schemes, utility approximations, and temperature and volume regimes. Analogies to ideal classical and quantum gases are found and features specific for network systems are discussed.Comment: The Eur. Phys. J. B, in prin

A model for effective interactions in binary colloidal systems of soft particles

While the density functional theory with integral equations techniques are very efficient tools in numerical analysis of complex fluids, an analytical insight into the phenomenon of effective interactions is still limited. In this paper we propose a theory of binary systems which results in a relatively simple analytical expression combining arbitrary microscopic potentials into the effective interaction. The derivation is based on translating many particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language. Such transformation turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. In result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the effective attraction as a demixing factor in the binary systems of Gaussian particles, effective interactions in the binary mixtures of Yukawa particles and the system of particles consisting of both repulsive core and attractive/repulsive Yukawa interaction tail, for which we reproduce the 'attraction-through-repulsion' and 'repulsion-through-attraction' effects.Comment: Second version of article, after major revision due to the comments from reviewers. Includes overhauled introductory section, new, more compact derivation and more elaborate examples than previousl

Thermodynamically consistent Langevin dynamics with spatially correlated noise predicts frictionless regime and transient attraction effect

While the origin of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of Spatially Correlated Noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, we derive the formal formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by SCN and the adequate Fluctuation-Dissipation Relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g. the singular behavior for certain interaction types. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a non-equilibrium mechanism facilitating the molecular binding of the like-charged particles.Comment: expanded and revised version resubmitted to Phys. Rev.

Non-Gaussian polymers described by alpha-stable chain statistics: model, applications and effective interactions in binary mixtures

The Gaussian chain model is the classical description of a polymeric chain, which provides the analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the alpha stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of alpha stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the alpha-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains with heavy-tailed distributions of persistence length, polymers adsorbed to the surface and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the alpha-stable chain and the coarse-grained interaction potential between two chains is constructed. These results are employed to discuss the model of binary mixture consisting of the alpha-stable chains. On what follows, we establish the spinodal decomposition condition generalized to the particles described by the shape of alpha-stable distributions. This condition is finally applied to analyze the on-surface phase separation of adsorbed polymers, which are known to be described with heavy tailed statistics.Comment: Complete version prepared for submission to Phys. Rev.

Quantitative contraction rates for Markov chains on general state spaces

We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently been derived by combining appropriate couplings with carefully designed Kantorovich distances. In this paper, we partially carry over this approach from diffusions to Markov chains. We derive quantitative lower bounds on contraction rates for Markov chains on general state spaces that are powerful if the dynamics is dominated by small local moves. For Markov chains on $\mathbb{R^d}$ with isotropic transition kernels, the general bounds can be used efficiently together with a coupling that combines maximal and reflection coupling. The results are applied to Euler discretizations of stochastic differential equations with non-globally contractive drifts, and to the Metropolis adjusted Langevin algorithm for sampling from a class of probability measures on high dimensional state spaces that are not globally log-concave.Comment: 39 page

Production of Stable and Unstable Nuclei and Hyperfragments in 11.5 A GeV/c Au+Pb collisions

We present measurements of the production of stable light nuclei for mass number A<=7, of strongly decaying states He(5) and Li(5) and of the hypernucleus H(3,lambda). We also examine trends in the production of these multibaryon states as a function of kinematic variables and properties of these states including strangeness content.Comment: Quark Matter '99 Conferenc

Do Field Crop Farms and Mixed Farms of Old and New EU Members Improve Productivity at the Same Rate? A Regional Level Approach

data contained in the Farm Accounting Data Network (FADN). Analyses covered the first four years following the extension of the European Union in 2004. The adopted units comprised average farms representing 80 regions belonging to eleven countries of EU-15 and four new EU member states. Estimation of the Malmquist total factor productivity (TFP) and its components was conducted using data envelopment analysis, separately for each of the two types of farms taking into consideration their economic size. The main findings concerning the pure technical efficiency change indicate that in the units from the old regions there was a slight improvement for field crop farms and stagnation for mixed farms, and a decrease in the units from the new regions, being bigger for mixed farms and smaller for field crop farms. The biggest effect was observed for the technical change index, with a bigger increase for crop farms from old regions than those from the new member states. The estimated Malmquist index confirms a conjecture that the more specialized farms more effectively improve overall productivity than mixed farms, where modernization efforts are more scattered. At the same time the average growth rate of TFP in crop farms from the EU-15 regions in the analyzed period was much faster that in analogous farms from the new regions. For mixed farms the difference in the rate of change was similar, but at a much lower level.data envelopment analysis, technical efficiency change, scale efficiency change, Malmquist index, Crop Production/Industries, Productivity Analysis,