Pragmatist Perspectives on Theological and Religious Realism

This essay first applies the general issue of realism vs. antirealism to theology and the philosophy of religion, distinguishing between several different ”levels’ of the realism dispute in this context. A pragmatic approach to the problem of realism regarding religion and theology is sketched and tentatively defended. The similarities and differences of scientific realism, on the one hand, and religious and/or theological realism, on the other hand, are thereby also illuminated. The concept of recognition is shown to be crucially relevant to the issue of realism especially in its pragmatist articulation

Gaussian estimates for spatially inhomogeneous random walks on Zd{\mathbf{Z}}^d

It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on ${\mathbf{Z}}^d$ admits upper and lower Gaussian estimates.Comment: Published at http://dx.doi.org/10.1214/009117905000000440 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A combinatorial realization of Schur-Weyl duality via crystal graphs and dual equivalence graphs

For any polynomial representation of the special linear group, the nodes of the corresponding crystal may be indexed by semi-standard Young tableaux. Under certain conditions, the standard Young tableaux occur, and do so with weight 0. Standard Young tableaux also parametrize the vertices of dual equivalence graphs. Motivated by the underlying representation theory, in this paper, we explainthis connection by giving a combinatorial manifestation of Schur-Weyl duality. In particular, we put a dual equivalence graph structure on the 0-weight space of certain crystal graphs, producing edges combinatorially from the crystal edges. The construction can be expressed in terms of the local characterizations given by Stembridge for crystal graphs and the author for dual equivalence graphs.Comment: 9 pages, 6 figures To appear in DMTCS as part of the FPSAC 2008 conference proceeding