Regulation mechanisms in spatial stochastic development models

The aim of this paper is to analyze different regulation mechanisms in spatial continuous stochastic development models. We describe the density behavior for models with global mortality and local establishment rates. We prove that the local self-regulation via a competition mechanism (density dependent mortality) may suppress a unbounded growth of the averaged density if the competition kernel is superstable.Comment: 19 page

Correlation functions evolution for the Glauber dynamics in continuum

We construct a correlation functions evolution corresponding to the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we prove the existence of the evolution of states and study their ergodic properties

Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials

We study the existence of stationnary positive solutions for a class of nonlinear Schroedinger equations with a nonnegative continuous potential V. Amongst other results, we prove that if V has a positive local minimum, and if the exponent of the nonlinearity satisfies N/(N-2)<p<(N+2)/(N-2), then for small epsilon the problem admits positive solutions which concentrate as epsilon goes to 0 around the local minimum point of V. The novelty is that no restriction is imposed on the rate of decay of V. In particular, we cover the case where V is compactly supported.Comment: 22 page

Gauge-Invariant Quasi-Free States on the Algebra of the Anyon Commutation Relations

Let $X=\mathbb R^2$ and let $q\in\mathbb C$, $|q|=1$. For $x=(x^1,x^2)$ and $y=(y^1,y^2)$ from $X^2$, we define a function $Q(x,y)$ to be equal to $q$ if $x^1y^1$, and to $\Re q$ if $x^1=y^1$. Let $\partial_x^+$, $\partial_x^-$ ($x\in X$) be operator-valued distributions such that $\partial_x^+$ is the adjoint of $\partial_x^-$. We say that $\partial_x^+$, $\partial_x^-$ satisfy the anyon commutation relations (ACR) if $\partial^+_x\partial_y^+=Q(y,x)\partial_y^+\partial_x^+$ for $x\ne y$ and $\partial^-_x\partial_y^+=\delta(x-y)+Q(x,y)\partial_y^+\partial^-_x$ for $(x,y)\in X^2$. In particular, for $q=1$, the ACR become the canonical commutation relations and for $q=-1$, the ACR become the canonical anticommutation relations. We define the ACR algebra as the algebra generated by operator-valued integrals of $\partial_x^+$, $\partial_x^-$. We construct a class of gauge-invariant quasi-free states on the ACR algebra. Each state from this class is completely determined by a positive self-adjoint operator $T$ on the real space $L^2(X,dx)$ which commutes with any operator of multiplication by a bounded function $\psi(x^1)$. In the case $\Re q0$), we discuss the corresponding particle density $\rho(x):=\partial_x^+\partial_x^-$. For $\Re q\in(0,1]$, using a renormalization, we rigorously define a vacuum state on the commutative algebra generated by operator-valued integrals of $\rho(x)$. This state is given by a negative binomial point process. A scaling limit of these states as $\kappa\to\infty$ gives the gamma random measure, depending on parameter $\Re q$

Laplace Operators in Gamma Analysis

a

Stochastic dynamics for an infinite system of random closed strings: a Gibbsian point of view

We consider the stochastic dynamics of infinitely many, interacting random closed strings, and show that the law of this process can be characterized as a Gibbs state for some Hamiltonian on the path level, which is represented in terms of the interaction. This is done by means of the stochastic calculus of variations, in particular an integration by parts formula in infinite dimensions. This Gibbsian point of view of the stochastic dynamics allows us to characterize under monothonicity conditions, the reversible states as the Gibbs states for the underlying interaction. Since in our situation there is only one stationary distribution, we see that there is exactly one such Gibbs state. (orig.)Available from TIB Hannover: RO 5073(632/5) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Transverse momentum spectra of charged particles in proton-proton collisions at 1as=900 GeV with ALICE at the LHC

The inclusive charged particle transverse momentum distribution is measured in proton-proton collisions at s=900 GeV at the LHC using the ALICE detector. The measurement is performed in the central pseudorapidity region (|\u3b7|<0.8) over the transverse momentum range 0.15<10 GeV/c. The correlation between transverse momentum and particle multiplicity is also studied. Results are presented for inelastic (INEL) and non-single-diffractive (NSD) events. The average transverse momentum for |\u3b7|<0.8 is \u3008pT\u3009INEL=0.483\ub10.001 (stat.)\ub10.007 (syst.) GeV/c and \u3008pT\u3009NSD=0.489\ub10.001 (stat.)\ub10.007 (syst.) GeV/c, respectively. The data exhibit a slightly larger \u3008pT\u3009 than measurements in wider pseudorapidity intervals. The results are compared to simulations with the Monte Carlo event generators PYTHIA and PHOJET. \ua9 2010