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

UR - http://www.scopus.com/inward/record.url?scp=85090617323&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85090617323&partnerID=8YFLogxK

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 -