MathPhysicsHarmonic Analysis Seminar, October 15th 2003
Professor Stanislav Molchanov (UNCC)
Shape theorem for the Anderson parabolic problem and the theory of
random polymers
Abstract: The Anderson parabolic problem
∂H
= k∆H + V H, H(0, x) ≡ 1, x ∈ Rn
∂t
(1)
with a random spatially homogeneous potential V describes magnetic phenomena (the dynamo process) and chemical kinetics in a random environment. Potential V can be either time independent (statistically random
medium), or δ-correlated in time (turbulent medium). If initial data are localized, say H(0, x) = δ(x) , then the solution represents the distribution of a
random polymer growing in the random potential field V (·) (a stationary or
turbulent one). Then the equation (1) is associated with the KPZ - equation,
well known in the physics literature.
The talk will present recent results on the shape of the solution H(t, ∗)
when t → ∞ and discussion of some open problems.
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