TY - CHAP
T1 - The polaron measure
AU - Mukherjee, Chiranjib
AU - Varadhan, S. R.S.
N1 - Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2020.
PY - 2020
Y1 - 2020
N2 - {x(t) − x(s)} are the increments of the three dimensional Brownian motion over the intervals [s, t]. (Formula Presented). Qα,T is defined as the measure with Radon–Nikodym derivative [Z(T, α)]−1 exp [αF(T, ω)] with respect to Brownian Motion, Z(α, T) being the normalization constant Z(T, α) = E[exp [αF(T, ω)]]. We are interested in the existence of the Polaron measure Qα =limT→∞Qα,T, the validity of central limit theorem for (Formula Presented) under Qα,T as well as Qα and the behavior of Qα for large α.
AB - {x(t) − x(s)} are the increments of the three dimensional Brownian motion over the intervals [s, t]. (Formula Presented). Qα,T is defined as the measure with Radon–Nikodym derivative [Z(T, α)]−1 exp [αF(T, ω)] with respect to Brownian Motion, Z(α, T) being the normalization constant Z(T, α) = E[exp [αF(T, ω)]]. We are interested in the existence of the Polaron measure Qα =limT→∞Qα,T, the validity of central limit theorem for (Formula Presented) under Qα,T as well as Qα and the behavior of Qα for large α.
KW - Birth death process
KW - Gaussian process
KW - Polaron measure
KW - Regeneration property
KW - White noise
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U2 - 10.1007/978-981-15-5951-8_24
DO - 10.1007/978-981-15-5951-8_24
M3 - Chapter
AN - SCOPUS:85090617323
T3 - Infosys Science Foundation Series in Mathematical Sciences
SP - 415
EP - 419
BT - Infosys Science Foundation Series in Mathematical Sciences
PB - Springer
ER -