The asymmetric ABAB matrix model

In this letter, it is pointed out that the two matrix model defined by the action S=(1/2)(tr A^2+tr B^2)-(alpha_A/4) tr A^4-(alpha_B/4) tr B^4-(beta/2) tr(AB)^2 can be solved in the large N limit using a generalization of the solution of Kazakov and Zinn-Justin (who considered the symmetric case alpha_A=alpha_B). This model could have useful applications to 3D Lorentzian gravity.Comment: 7 pages, 1 figur

The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links

The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding ``renormalization equations'' are derived. Some particular cases are studied in detail and solved exactly.Comment: 21 page

The Limits of an Egalitarian Ethos: G. A. Cohen's Critique of Rawlsian Liberalism

G.A. Cohen’s critique of the Rawlsian difference principle points out an inconsistency in its presentation. The initial equality decided by the participants in the original position under the veil of ignorance is not preserved by the inequality sanctioned by the difference principle. Cohen shows how the breakdown of the initial equality of the original position prevents the desired results of the Rawlsian system from being realized. Cohen argues that an egalitarian ethos is required within a society for equality preserving economic distributions and Pareto superior outcomes to occur. Nonetheless, Cohen’s analysis of Rawls misses the ultimate cause of inequality, which is the dynamics of capital accumulation. An egalitarian ethos is only possible if there is a socialist mode of production to facilitate its development. Additionally, Cohen’s critique of Rawlsian constructivism through an argument for intuitionism does not address the natural-material existence of human beings. This existence must be considered for any advantageous social formation

Proof of Razumov-Stroganov conjecture for some infinite families of link patterns

We prove the Razumov--Stroganov conjecture relating ground state of the O(1) loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches, for which we use as key ingredient of the proof a generalization of the Mac Mahon formula for the number of plane partitions which includes three series of parameters

Jucys-Murphy elements and Weingarten matrices

We provide a compact proof of the recent formula of Collins and Matsumoto for the Weingarten matrix of the orthogonal group using Jucys-Murphy elements.Comment: v2: added a referenc