The time evolution of permutations under random stirring

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 $n\to\infty$.Comment: 15 page

Van Til versus Stroud: Is the Transcendental Argument for Christian Theism Viable?

In this paper I introduce the transcendental argument for Christian theism in the context of Reformed theologian and philosopher Cornelius Van Til’s thought. I then present the critique proffered by Barry Stroud against ambitious transcendental arguments, and survey various formulations of transcendental arguments in the literature, seeking how the objection bears upon them. I argue that Adrian Bardon’s (2005) interpretation is the most helpful in understanding the Stroudian objection. From this interpretation, two types of possible rebuttals are deduced. Proceeding to survey the responses offered by Van Tillians to this objection in the recent literature, I discern two general strategies pursued in these responses, which map onto the previously deduced types of rebuttals: the Biblical justification strategy and the objection-undermining strategy. I argue that all the specific attempts to answer Stroud which I examine here (those of Butler, Bosserman, and Fluhrer) are inadequate and that these two strategies, in general, face serious problems. I conclude with considering the options before the proponent of the transcendental argument for Christian theism and with offering a new objection to the argument, which focuses on its inconsistency with the implications of Christian theism itself

Diffusive and Super-Diffusive Limits for Random Walks and Diffusions with Long Memory

We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field, modelling the motion of a particle suspended in time-stationary incompressible turbulent flow. The second class consists of self-repelling random diffusions, where the diffusing particle is pushed by the negative gradient of its own occupation time measure towards regions less visited in the past. We establish normal diffusion (with square-root-of-time scaling and Gaussian limiting distribution) in three and more dimensions and typically anomalously fast diffusion in low dimensions (typically, one and two). Results are quoted from various papers published between 2012-2018, with some hints to the main ideas of the proofs. No technical details are presented here.Comment: ICM-2018 Probability Section tal

Tracy-Widom limit of q-Hahn TASEP

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.Comment: 23 pages, 3 figure

On the bipartite graph packing problem

The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences

The Country-specific Organizational and Information Architecture of ERP Systems at Globalised Enterprises

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.Information System; ERP; Enterprise Resource Planning; Enterprise Architecture; Globalization; Centralization; Decentralization; Hybrid