Peer-reviewedCC BYCommunications in Mathematical Physics
Linear Fluctuation of Interfaces in Glauber–Kawasaki Dynamics
Abstract
In this article, we find a scaling limit of the space-time mass fluctuation field of Glauber + Kawasaki particle dynamics around its hydrodynamic mean curvature interface limit. Here, the Glauber rates are scaled by K=KN K = K N (with KN↑ ∞ K N ↑ ∞ as N↑ ∞ N ↑ ∞ ), the Kawasaki rates by N2 N 2 and space by 1/ N . We start the process so that the continuum interface Γ t Γ t formed, between ‘high’ ρ + ρ + and ‘low’ ρ - ρ - density regions, is stationary that is, Γ t Γ t is ‘flat’. When the Glauber rates are balanced on 𝕋d T d , the interface Γ t=Γ ={v: v1=0} Γ t = Γ = { v : v 1 = 0 } is immobile and the hydrodynamic limit is given by ρ (t,v) = ρ + ρ ( t , v ) = ρ + for v1∈ (0,1/2) v 1 ∈ ( 0 , 1 / 2 ) and ρ (t,v)= ρ - ρ
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BibTeX
@article{funaki2026linear,
title = {{Linear Fluctuation of Interfaces in Glauber–Kawasaki Dynamics}},
author = {Tadahisa Funaki and Claudio Landim and Sunder Sethuraman},
journal = {Communications in Mathematical Physics},
year = {2026},
month = sep,
doi = {10.1007/s00220-026-05712-3},
eprint = {2412.04015},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05770829v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Linear Fluctuation of Interfaces in Glauber–Kawasaki Dynamics
AU - Tadahisa Funaki
AU - Claudio Landim
AU - Sunder Sethuraman
PY - 2026
DA - 2026/09/27
JO - Communications in Mathematical Physics
DO - 10.1007/s00220-026-05712-3
UR - https://hal.science/hal-05770829v1
AB - In this article, we find a scaling limit of the space-time mass fluctuation field of Glauber + Kawasaki particle dynamics around its hydrodynamic mean curvature interface limit. Here, the Glauber rates are scaled by K=K_N K = K N (with K_N↑ ∞ K N ↑ ∞ as N↑ ∞ N ↑ ∞ ), the Kawasaki rates by N^2 N 2 and space by 1/ N . We start the process so that the continuum interface Γ _t Γ t formed, between ‘high’ ρ _+ ρ + and ‘low’ ρ _- ρ - density regions, is stationary that is, Γ _t Γ t is ‘flat’. When the Glauber rates are balanced on 𝕋^d T d , the interface Γ _t=Γ ={v: v_1=0} Γ t = Γ = { v : v 1 = 0 } is immobile and the hydrodynamic limit is given by ρ (t,v) = ρ _+ ρ ( t , v ) = ρ + for v_1∈ (0,1/2) v 1 ∈ ( 0 , 1 / 2 ) and ρ (t,v)= ρ _- ρ
SN - 0010-3616
SN - 1432-0916
ER -