1,175 research outputs found
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
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