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We obtain spectral estimates for the iterations of Ruelle operator $L_{f + (a + i b)tau + (c + i d) g}$ with two complex parameters and H{o}lder functions $f,: g$ generalizing the case $Pr(f) =0$ studied in [PeS2]. As an application we prove a sharp large deviation theorem concerning exponentially shrinking intervals which improves the result in [PeS1].
For hyperbolic flows $varphi_t$ we examine the Gibbs measure of points $w$ for which $$int_0^T G(varphi_t w) dt - a T in (- e^{-epsilon n}, e^{- epsilon n})$$ as $n to infty$ and $T geq n$, provided $epsilon > 0$ is sufficiently small. This is simila
We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - and therefore on the volume of the domain - must fail. Here we present a
Consider first passage percolation with identical and independent weight distributions and first passage time ${rm T}$. In this paper, we study the upper tail large deviations $mathbb{P}({rm T}(0,nx)>n(mu+xi))$, for $xi>0$ and $x eq 0$ with a time co
For non-critical almost Mathieu operators with Diophantine frequency, we establish exponential asymptotics on the size of spectral gaps, and show that the spectrum is homogeneous. We also prove the homogeneity of the spectrum for Schodinger operators
For diffusive many-particle systems such as the SSEP (symmetric simple exclusion process) or independent particles coupled with reservoirs at the boundaries, we analyze the density fluctuations conditioned on current integrated over a large time. We