TY - JOUR

T1 - A uniform estimate for rate functions in large deviations

AU - Stoyanov, Luchezar

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Given Hölder continuous functions f and ψ on a subshift of finite type ΣA+ such that ψ is not cohomologous to a constant, the classical large deviation principle holds with a rate function Iψ⩾ 0 such that Iψ(p) = 0 iff [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.] is the equilibrium state of f. In this paper we derive a uniform estimate from below for Iψ for p outside an interval containing [InlineEquation not available: see fulltext.], which depends only on the subshift ΣA+, the function f, the norm |ψ| ∞, the Hölder constant of ψ and the integral ψ~. Similar results can be derived in the same way, e.g. for Axiom A diffeomorphisms on basic sets.

AB - Given Hölder continuous functions f and ψ on a subshift of finite type ΣA+ such that ψ is not cohomologous to a constant, the classical large deviation principle holds with a rate function Iψ⩾ 0 such that Iψ(p) = 0 iff [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.] is the equilibrium state of f. In this paper we derive a uniform estimate from below for Iψ for p outside an interval containing [InlineEquation not available: see fulltext.], which depends only on the subshift ΣA+, the function f, the norm |ψ| ∞, the Hölder constant of ψ and the integral ψ~. Similar results can be derived in the same way, e.g. for Axiom A diffeomorphisms on basic sets.

KW - Equilibrium state

KW - Large deviations

KW - Rate function

KW - Subshift of finite type

UR - http://www.scopus.com/inward/record.url?scp=84995642346&partnerID=8YFLogxK

U2 - 10.1007/s40879-016-0119-z

DO - 10.1007/s40879-016-0119-z

M3 - Article

AN - SCOPUS:84995642346

VL - 2

SP - 1013

EP - 1022

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 4

ER -