TY - GEN
T1 - Stable Limit Laws for Reaction-Diffusion in Random Environment
AU - Ben Arous, Gérard
AU - Molchanov, Stanislav
AU - Ramírez, Alejandro F.
N1 - Funding Information:
Gérard Ben Arous: Partially supported by NSF DMS1209165 and BSF 2014019. Alejandro F. Ramírez: Partially supported by Fondo Nacional de Desarrollo Científico y Tecnológico 1141094 and 1180259 and Iniciativa Científica Milenio.
Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
N2 - We prove the emergence of stable fluctuations for reaction-diffusion in random environment with Weibull tails. This completes our work around the quenched to annealed transition phenomenon in this context of reaction diffusion. In Ben Arous et al (Transition asymptotics for reaction-diffusion in random media. Probability and mathematical physics, American Mathematical Society, Providence, RI, pp 1–40, 2007, [8]), we had already considered the model treated here and had studied fully the regimes where the law of large numbers is satisfied and where the fluctuations are Gaussian, but we had left open the regime of stable fluctuations. Our work is based on a spectral approach centered on the classical theory of rank-one perturbations. It illustrates the gradual emergence of the role of the higher peaks of the environments. This approach also allows us to give the delicate exact asymptotics of the normalizing constants needed in the stable limit law.
AB - We prove the emergence of stable fluctuations for reaction-diffusion in random environment with Weibull tails. This completes our work around the quenched to annealed transition phenomenon in this context of reaction diffusion. In Ben Arous et al (Transition asymptotics for reaction-diffusion in random media. Probability and mathematical physics, American Mathematical Society, Providence, RI, pp 1–40, 2007, [8]), we had already considered the model treated here and had studied fully the regimes where the law of large numbers is satisfied and where the fluctuations are Gaussian, but we had left open the regime of stable fluctuations. Our work is based on a spectral approach centered on the classical theory of rank-one perturbations. It illustrates the gradual emergence of the role of the higher peaks of the environments. This approach also allows us to give the delicate exact asymptotics of the normalizing constants needed in the stable limit law.
KW - Principal eigenvalue
KW - Random walk
KW - Rank one perturbation theory
KW - Stable distributions
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U2 - 10.1007/978-3-030-15338-0_5
DO - 10.1007/978-3-030-15338-0_5
M3 - Conference contribution
AN - SCOPUS:85068985156
SN - 9783030153373
T3 - Springer Proceedings in Mathematics and Statistics
SP - 123
EP - 171
BT - Probability and Analysis in Interacting Physical Systems - In Honor of S.R.S. Varadhan, 2016
A2 - Friz, Peter
A2 - König, Wolfgang
A2 - Mukherjee, Chiranjib
A2 - Olla, Stefano
PB - Springer New York LLC
T2 - Conference in Honor of the 75th Birthday of S.R.S. Varadhan, 2016
Y2 - 15 August 2016 through 19 August 2016
ER -