Tableaux and the Asymmetric Simple Exclusion Process

Various types of tableaux have recently been introduced due to a connection with the asymmetric simple exclusion process (ASEP) and have been the object of study in many recent papers. Relevant to this thesis, there have been several conjectures made regarding two such types of tableaux, namely staircase tableaux and tree--like tableaux. This thesis confirms these conjectures while proving other interesting results. More specifically, Hitczenko and Janson proved that distribution of symbols on the first diagonal of staircase tableaux is asymptotically normal, and they conjectured that other diagonals would be asymptotically Poisson. This thesis proves that conjecture for the kth diagonal where k is fixed. In addition, Laborde Zubieta gave a conjecture on the total number of corners in tree--like tableaux and the total number of corners in symmetric tree--like tableaux. Both conjectures are proven in this thesis. The proofs of these two conjectures are based on bijections with permutation tableaux and type--B permutation tableaux and consequently, results for these tableaux are also given. In addition, the limiting distributions of the number of occupied corners in tree--like tableaux and the number of diagonal boxes in symmetric tree--like tableaux are derived. These theorems extend results of Laborde-Zubieta and Aval et al. respectively.Ph.D., Mathematics -- Drexel University, 201

Tuning a two-impurity Kondo system by a moir\'e superstructure

Two-impurity Kondo models are paradigmatic for correlated spin-fermion systems. Working with Mn atoms on Au(111) covered by a monolayer of MoS$_2$, we tune the inter-adatom exchange via the adatom distance and the adatom-substrate exchange via the location relative to a moir\'e structure of the substrate. Differential-conductance measurements on isolated adatoms exhibit Kondo peaks with heights depending on the adatom location relative to the moir\'e structure. Mn dimers spaced by a few atomic lattice sites exhibit split Kondo resonances. In contrast, adatoms in closely spaced dimers couple antiferromagnetically, resulting in a molecular-singlet ground state. Exciting the singlet-triplet transition by tunneling electrons, we find that the singlet-triplet splitting is surprisingly sensitive to the moir\'e structure. We interpret our results theoretically by relating the variations in the singlet-triplet splitting to the heights of the Kondo peaks of single adatoms, finding evidence for coupling of the adatom spin to multiple conduction electron channels

Die Ornithin-Carbamyl-Transferase als Diagnostikum von Hepatopathien des Hundes

Available from: Zentralstelle fuer Agrardokumentation und -information (ZADI), Villichgasse 17, D-53177 Bonn / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Effects of the Presence of Another Person in Evaluative and Nonevaluativeroles on the Performance of Psychiatric Patients and Nonpatients

97 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1970.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Probabilistic consequences of some polynomial recurrences

© 2018 Wiley Periodicals, Inc. In this paper, we consider sequences of polynomials that satisfy certain recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. In particular, we will use our approach to show that the number of diagonal boxes in symmetric tree-like tableaux is asymptotically normal. This extends earlier results of Aval, Boussicault and Nadeau, who found the asymptotics of the expected number of diagonal boxes. Through our discussion, we establish a general framework to approach such recurrences and prompt a generalization of the probabilistic consequences of them