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

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

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

Independence ratio and random eigenvectors in transitive graphs

A theorem of Hoffman gives an upper bound on the independence ratio of regular graphs in terms of the minimum $\lambda_{\min}$ of the spectrum of the adjacency matrix. To complement this result we use random eigenvectors to gain lower bounds in the vertex-transitive case. For example, we prove that the independence ratio of a $3$-regular transitive graph is at least $$q=\frac{1}{2}-\frac{3}{4\pi}\arccos\biggl(\frac{1-\lambda _{\min}}{4}\biggr).$$ The same bound holds for infinite transitive graphs: we construct factor of i.i.d. independent sets for which the probability that any given vertex is in the set is at least $q-o(1)$. We also show that the set of the distributions of factor of i.i.d. processes is not closed w.r.t. the weak topology provided that the spectrum of the graph is uncountable.Comment: Published at http://dx.doi.org/10.1214/14-AOP952 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

What is the Future of Strategic Management?

The history of planning and creating strategies has a past of over half a century. Throughout this lifetime period we have witnessed both the evolution of theory and practice. The MBA study books in the last-third of the 20th century have with predilection exhibited this very process as a complex of monetary centered budget planning, forecast-based planning, strategic planning and strategic management. There might be a controversy existing about the naming, characteristics and timing of these different sections but there is an accordance that the changes that we have taken place in the last decade as a whole without a doubt can be derived from these very changes in the business environment or in some outstanding cases (like 9/11) they can be acknowledged as the ability of corporate foreseeing and the ability to adapt to the vision of the future. The main purposes of the research is to provide a summarized picture about the changing process of this procedure during last decades as far as the planning and creating strategies are concerned and also their milestones and periods. Try to explore and systemize the very aspects of these changes. The happenings of the first decade of the new millennium are outstandingly interesting if we consider their real effect on the theory and practice of strategic management. Let us remember the euphoria around the year 2000, the predictions of „new technologies”, „new economy”, „new organization” and „new leadership”. We have implied before on the destruction of the twin towers of the World Trade Center which meant a new era, a new quality of international terrorism and its consequences (Afghanistan, Iraq). But the „product” of this decade is the strategic aim that companies focus on, which is the social responsibility regarding the unavoidance of the effects of climate change on the long run. During the research the big question has risen concerning how did the science of strategic management do as far as the predictions of the global monetary and economic crisis are concerned? And also its solutions this very science has to offer in order to handle and get over the crisis. Does it conclude from the answers given to the questions that a change in paradigms are necessary, a new quality is needed or may be we have come to a new crossroad of the development process that will take over strategic management? (...

A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes

We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix $T_0$. Focusing on the eigenvalues of $T_0$ of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required $T_0$ to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schr\"odinger operators we can improve some result by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular we solve a problem posed in their work.Comment: new version, parts rearrange

The periodic decomposition problem

If a function $f:\mathbb{R}\to\mathbb{R}$ can be represented as the sum of $n$ periodic functions as $f=f_1+\dots+f_n$ with $f(x+\alpha_j)=f(x)$ ($j=1,\dots,n$), then it also satisfies a corresponding $n$-order difference equation $\Delta_{\alpha_1}\dots\Delta_{\alpha_n} f=0$. The periodic decomposition problem asks for the converse implication, which may hold or fail depending on the context (on the system of periods, on the function class in which the problem is considered, etc.). The problem has natural extensions and ramifications in various directions, and is related to several other problems in real analysis, Fourier and functional analysis. We give a survey about the available methods and results, and present a number of intriguing open problems

The bead process for beta ensembles

The bead process introduced by Boutillier is a countable interlacing of the determinantal sine-kernel point processes. We construct the bead process for general sine beta processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite beta corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian unitary and orthogonal ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper