Abstract:
We consider permutations of $\{1,...,n\}$ obtained by $\lfloor\sqrt{n}t\rfloor$ independent applications of random stirring. In each step the same marked stirring element is transposed with probability $1/n$ with any one of the $n$ elements. Normalizing by $\sqrt{n}$ we describe the asymptotic distribution of the cycle structure of these permutations, for all $t\ge 0$, as $n\to\infty$.

Abstract:
We consider the q-Hahn TASEP which is a three-parameter family of discrete time interacting particle systems. The particles jump to the right independently according to a certain q-Binomial distribution with parallel updates. It is a generalization of the discrete time q-TASEP which is the q-deformed totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1). For step initial condition, we prove that the current fluctuation of q-Hahn TASEP at time t is of order $t^{1/3}$ and asymptotically distributed as the GUE Tracy-Widom distribution. We verify the KPZ scaling theory conjecture for the q-Hahn TASEP.

Abstract:
A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches the hard edge, a limiting critical process is described in the neighbourhood of the touching point which we call the hard edge tacnode process. We derive its correlation kernel in an explicit new form which involves Airy type functions and operators that act on the direct sum of $L^2(\mathbb R_+)$ and a finite dimensional space. As the starting points of the squared Bessel paths are set to 0, a cusp in the boundary appears. The limiting process is described near the cusp and it is called the hard edge Pearcey process. We compute its multi-time correlation kernel which extends the existing formulas for the single-time kernel. Our pre-asymptotic correlation kernel involves the ratio of two Toeplitz determinants which are rewritten using a Borodin-Okounkov type formula.

Abstract:
We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for k=1,2,... and for the probability that the record of the kth longest age is broken at step n. Furthermore, we show that the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

Abstract:
We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulae are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.

Abstract:
the genus airamanna gen. n. (type species: annamaria columbia bálint, 2005) is established on the basis of characters provided by male ventral forewing surface (blue reflector and dorsal androconia) and sexually dimorphic ventral wing colouration and pattern. the genus contains three species, which can be distinguished on the basis of male dorsal forewing androconia: a. columbia (bálint, 2005), new combination, with extensive dorsal forewing postbasal and postdiscal androconia (columbia); a. rhapsodia (bálint, 2005), new combination, with extensive hindwing postbasal androconia (bolivia) and a. rhaptissima (johnson, 1991), new combination, with reduced androconia in both dorsal wing surfaces (ecuador and peru). in colombia a. columbia is recorded from the regions cauca-muchique, nari？o and valle.

Abstract:
The competition on the market forces companies to adapt to the changing environment. Most recently, the economic and financial crisis has been accelerating the alteration of both business and IT models of enterprises. The forces of globalization and internationalization motivate the restructuring of business processes and consequently IT processes. To depict the changes in a unified framework, we need the concept of Enterprise Architecture as a theoretical approach that deals with various tiers, aspects and views of business processes and different layers of application, software and hardware systems. The paper outlines a wide-range theoretical background for analyzing the re-engineering and re-organization of ERP systems at international or transnational companies in the middle-sized EU member states. The research carried out up to now has unravelled the typical structural changes, the models for internal business networks and their modification that reflect the centralization, decentralization and hybrid approaches. Based on the results obtained recently, a future research program has been drawn up to deepen our understanding of the trends within the world of ERP systems.

Abstract:
For a given bi-continuous semigroup T on a Banach space X we define its adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology (X^o,X). An application is the following: For K a Polish space we consider operator semigroups on the space C(K) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(K) of bounded Baire measures (endowed with the weak*-topology). We show that bi-continuous semigroups on M(K) are precisely those that are adjoints of a bi-continuous semigroups on C(K). We also prove that the class of bi-continuous semigroups on C(K) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. In general, if K is not Polish space this is not the case.

Abstract:
For parameters $p\in[0,1]$ and $q>0$ such that the Fortuin--Kasteleyn (FK) random-cluster measure $\Phi_{p,q}^{\mathbb{Z}^d}$ for $\mathbb{Z}^d$ with parameters $p$ and $q$ is unique, the $q$-divide and color [$\operatorname {DaC}(q)$] model on $\mathbb{Z}^d$ is defined as follows. First, we draw a bond configuration with distribution $\Phi_{p,q}^{\mathbb{Z}^d}$. Then, to each (FK) cluster (i.e., to every vertex in the FK cluster), independently for different FK clusters, we assign a spin value from the set $\{1,2,\...,s\}$ in such a way that spin $i$ has probability $a_i$. In this paper, we prove that the resulting measure on spin configurations is a Gibbs measure for small values of $p$ and is not a Gibbs measure for large $p$, except in the special case of $q\in \{2,3,\...\}$, $a_1=a_2=\...=a_s=1/q$, when the $\operatorname {DaC}(q)$ model coincides with the $q$-state Potts model.

Abstract:
We prove that a separable Banach space $E$ does not contain a copy of the space $\co$ of null-sequences if and only if for every doubly power-bounded operator $T$ on $E$ and for every vector $x\in E$ the relative compactness of the sets $\{T^{n+m}x-T^nx: n\in \NN\}$ (for some/all $m\in\NN$, $m\geq 1$) and $\{T^nx:n\in \NN\}$ are equivalent. With the help of the Jacobs--de Leeuw--Glicksberg decomposition of strongly compact semigroups the case of (not necessarily invertible) power-bounded operators is also handled.