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math.PR2023
Onset of pattern formation for the stochastic Allen-Cahn equation
Stella Brassesco, Glauco Valle, Maria Eulália Vares
We study the behavior of the solution of a stochastic Allen-Cahn equation $\frac{\partial u_\eps }{\partial t}=\frac 12 \frac{\partial^2 u_\eps }{\partial x^2}+ u_\eps -u_\eps^3+\s…
math.PR2012
On the density of the winding number of planar Brownian motion
Stella Brassesco, Silvana C. García Pire
We obtain a formula for the density of the winding number of planar Brownian motion around the origin, and deduce from it asymptotic expansions in inverse powers of the logarithm o…