The growth exponent for planar loop-erased random walk

We give a new proof of a result of Kenyon that the growth exponent for loop-erased random walks in two dimensions is 5/4. The proof uses the convergence of LERW to Schramm-Loewner evolution with parameter 2, and is valid for irreducible bounded symmetric random walks on any two-dimensional discrete lattice.Comment: 62 pages, 7 figures; fixed typos, added reference

Rahner\u27s Primordial Words and Bernstein\u27s Metaphorical Leaps: The Affinity of Art with Religion and Theology

Karl Rahner\u27s notion of primordial words and Leonard Bernstein\u27s conception of music as intrinsically metaphorical are engaged to suggest that there is a fundamental affinity between artistic and religious imagination. The affinity is grounded, in part at least, in metaphoric process—an elemental cognitive act in which the human spirit is stretched so that its expressions can address what lies beyond them

Analogy as Higher-Order Metaphor in Aquinas

At a Thomas Instituut conference in 2000, Otto-Hermann Pesch suggested somewhat enigmatically that the sharp distinction in scholastic Thomism between analogy and metaphor can no longer be maintained since on closer examination analogous statements are in effect instances of a kind of \u27higher-order metaphor\u27. I Pesch intended this qualification primarily to draw attention to the agnostic or negative aspect of analogous speech.2 It is evident from Herwi Rikhof\u27s portrait of \u27Thomas at Utrecht\u27 ,3 that this emphasis on the negative dimension did not introduce anything controversial or novel at the Instituut