Vicious Walkers and Hook Young Tableaux

We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy--Widom distribution, which is same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.Comment: 23 pages, 5 figure

Best-shot versus weakest-link in political lobbying: an application of group all-pay auction

We analyze a group political lobbying all-pay auction with a group specific public good prize, in which one group follows a weakest-link and the other group follows a best-shot impact function. We completely characterize all semi-symmetric equilibria. There are two types of equilibria: (1) each player in the best-shot group puts mass at the upper bound of the support, whereas each player in the other group puts mass at the lower bound of the support; (2) players in the best-shot group put masses at both the lower and the upper bounds, while the other group randomizes without a mass point. An earlier and longer version of this study was circulated under the title “The Group All-pay Auction with Heterogeneous Impact Functions.” We appreciate the comments of an Associate Editor and two anonymous referees, Kyung Hwan Baik, Walter Enders, Matt Van Essen, Paan Jindapon, David Malueg, Paul Pecorino, Seth Streitmatter, Ted Turocy, the participants at the 2015 conference of ‘Contest: Theory and Evidence’ at the University of East Anglia, and the seminar participants at the University of Alabama and Korea University. Iryna Topolyan gratefully acknowledges the support from the Charles Phelps Taft Research Center. Any remaining errors are our own

On the partial connection between random matrices and interacting particle systems

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of large matrices arise also in the long time limit for interacting particles and growth models. Examples of these are the famous Tracy-Widom distribution functions and the Airy_2 process. The link is however sometimes fragile. For example, the connection between the eigenvalues in the Gaussian Orthogonal Ensembles (GOE) and growth on a flat substrate is restricted to one-point distribution, and the connection breaks down if we consider the joint distributions. In this paper we first discuss known relations between random matrices and the asymmetric exclusion process (and a 2+1 dimensional extension). Then, we show that the correlation functions of the eigenvalues of the matrix minors for beta=2 Dyson's Brownian motion have, when restricted to increasing times and decreasing matrix dimensions, the same correlation kernel as in the 2+1 dimensional interacting particle system under diffusion scaling limit. Finally, we analyze the analogous question for a diffusion on (complex) sample covariance matrices.Comment: 31 pages, LaTeX; Added a section concerning the Markov property on space-like path

Fermionic approach to the evaluation of integrals of rational symmetric functions

We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions, Two-Matrix Models and Biorthogonal Polynomials'' \cite{paper2}, where these integrals were evaluated by a direct method.Comment: 34 page

Model Reduction in Discrete Vortex Methods for 2D Unsteady Aerodynamic Flows

In this paper, we propose a method for model reduction in discrete-vortex methods. Discrete vortex methods have been successfully employed to model separated and unsteady airfoil flows. Earlier research revealed that a parameter called the Leading Edge Suction Parameter (LESP) can be used to model leading-edge vortex (LEV) shedding in unsteady flows. The LESP is a measure of suction developed at the leading edge, and whenever the LESP exceeds a critical value, a discrete vortex is released from the leading edge so as to keep the LESP at the critical value. Though the method was successful in predicting the forces on and the flow field around an airfoil in unsteady vortex-dominated flows,it was necessary to track a large number of discrete vortices in order to obtain the solution. The current study focuses on obtaining a model with a reduced number of leading-edge vortices, thus improving the computation time. Vortex shedding from the leading edge is modelled by a shear layer that comprises of a few discrete vortices, and a single concentrated vortex whose strength varies with time. The single vortex at the end of the shear layer accounts for the concentrated vortical structure that comprises several discrete vortex elements in conventional vortex methods. A merging algorithm is initiated when the edge of the shear layer starts rolling up. Suitable discrete vortices are identified using a kinematic criterion, and are merged to the growing vortex at every time step. The reduced order method is seen to bring down the number of discrete vortices shed from the leading edge significantly

THE TRANSFORMATIVE POTENTIAL OF CREATIVE ART PRACTICES IN THE CONTEXT OF INTERDISCIPLINARY RESEARCH

A growing body of literature addressing the need for educational innovations has also stressed the value of interdisciplinary approaches that incorporate art into teaching and learning. This paper aims to extend educators??? understanding of art???science interactions by presenting an empirical study that explores a unique art residency program created on the campus of a university that specializes in science and technology. The study reviews the art practices of three contemporary artists who participated in a program developed in conjunction with an interdisciplinary research project seeking ways to build an ecologically sustainable community and operated by a renewable energy resource-based economic system. Data that include observations, artist talks, and in-person interviews were collected from multiple sources during the residency to understand the distinguished processes involved in the development of individual art projects. A follow-up cross-case analysis revealed a few notable characteristics: connecting art with life through waste recycling, process-oriented practices highlighting resource circulation, and creating value using bricolage strategies. Regarding educational implications, discussions centered upon the potential transformational space identified from the creative art practices in the context of interdisciplinary research