ar X iv : m at h - ph / 0 31 20 01 v 1 2 9 N ov 2 00 3 On the edge universality of the local eigenvalue statistics of matrix models

ar X iv : m at h - ph / 0 31 10 01 v 4 3 N ov 2 00 4 Clifford Valued Differential Forms , Algebraic Spinor Fields

ar X iv : m at h - ph / 0 30 50 44 v 1 2 2 M ay 2 00 3 Universality for eigenvalue correlations at the origin of the spectrum

We establish universality of local eigenvalue correlations in unitary random matrix ensembles 1 Zn | det M | 2α e −ntr V (M) dM near the origin of the spectrum. If V is even, and if the recurrence coefficients of the orthogonal polynomials associated with |x| 2α e −nV (x) have a regular limiting behavior, then it is known from work of Akemann et al., and Kanzieper and Freilikher that the local ...

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : h ep - l at / 0 01 10 56 v 1 1 2 N ov 2 00 0 1 Asymptotically free theories based on discrete subgroups ∗ †

We study the critical behavior of discrete spin models related to the 2d O(3) non-linear sigma model. Precise numerical results suggest that models with sufficiently large discrete subgroups are in the same universality class as the original sigma model. We observe that at least up to correlation lengths ξ ≈ 300 the cut-off effects follow effectively an ∝ a behaviour both in the O(3) and in the...

ar X iv : m at h - ph / 0 31 10 29 v 1 2 0 N ov 2 00 3 Group theoretical approach to the intertwined Hamiltonians

We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relati...