TY - BOOK
T1 - Heat content and inradius for regions with a Brownian boundary
AU - Berg, van den, M.
AU - Bolthausen, E.
AU - Hollander, den, W.Th.F.
PY - 2013
Y1 - 2013
N2 - In this paper we consider \beta [0, s], Brownian motion of time length s > 0, in m-dimensional Euclidean space R^m and on the m-dimensional torus T^m. We compute the expectation of (i) the heat content at time t of R^m \ \beta [0, s] for fixed s and m = 2,3 in the limit t \downarrow 0, when \beta [0, s] is kept at temperature 1 for all t > 0 and R^m \ \beta [0, s] has initial temperature 0, and (ii) the inradius of T^m \ \beta [0, s] for m = 2,3,… in the limit s \rightarrow \infty.
Key words and phrases. Laplacian, Brownian motion, Wiener sausage, heat content, inradius, spectrum.
AB - In this paper we consider \beta [0, s], Brownian motion of time length s > 0, in m-dimensional Euclidean space R^m and on the m-dimensional torus T^m. We compute the expectation of (i) the heat content at time t of R^m \ \beta [0, s] for fixed s and m = 2,3 in the limit t \downarrow 0, when \beta [0, s] is kept at temperature 1 for all t > 0 and R^m \ \beta [0, s] has initial temperature 0, and (ii) the inradius of T^m \ \beta [0, s] for m = 2,3,… in the limit s \rightarrow \infty.
Key words and phrases. Laplacian, Brownian motion, Wiener sausage, heat content, inradius, spectrum.
M3 - Report
T3 - Report Eurandom
BT - Heat content and inradius for regions with a Brownian boundary
PB - Eurandom
CY - Eindhoven
ER -