Map Lattices Coupled by Collisions: Hitting Time Statistics and Collisions Per Lattice Unit

نویسندگان

چکیده

Abstract We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation model can be used to extract information about collisions per lattice unit. More precisely, we a on finite box L sites boundary conditions, collision. derive, via non-trivial first-order for leading eigenvalue rare event operator, formula first rate corresponding hitting time law . For former that scales at order $$L\cdot \varepsilon ^2$$ L · ε 2 , where $$\varepsilon $$ is coupling strength, latter, tracking dependency in our arguments, error $$O\left( C(L)\frac{L\varepsilon ^2}{\zeta (L)}\cdot \left| \ln \frac{L\varepsilon (L)}\right| \right) O C ( ) ζ ln $$\zeta (L)$$ given terms spectral gap C ( ) has an explicit expression. Finally, derive unit

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ژورنال

عنوان ژورنال: Annales Henri Poincaré

سال: 2022

ISSN: ['1424-0661', '1424-0637']

DOI: https://doi.org/10.1007/s00023-022-01164-2