scholarly journals Spectral rigidity and invariant distributions on Anosov surfaces

2014 ◽  
Vol 98 (1) ◽  
pp. 147-181 ◽  
Author(s):  
Gabriel P. Paternain ◽  
Mikko Salo ◽  
Gunther Uhlmann
Keyword(s):  
Invariant Distributions ◽  
Spectral Rigidity

Limiting conditional and conditional invariant distributions for the Poisson process with negative drift

1999 ◽  
Vol 36 (04) ◽  
pp. 1194-1209 ◽  
Author(s):  
Raúl Fierro ◽  
Servet Martínez ◽  
Jaime San Martín
Keyword(s):  
Initial Point ◽  
Time Process ◽  
Conditional Distributions ◽  
Exponential Law ◽  
Invariant Distributions ◽  
Virtual Waiting Time ◽  
The Family ◽  
Waiting Time Process ◽  
Negative Drift ◽  
Limiting Behaviour

In this paper we study the conditional limiting behaviour for the virtual waiting time process for the queue M/D/1. We describe the family of conditional invariant distributions which are continuous and parametrized by the eigenvalues λ ∊ (0, λ c ], as it happens for diffusions. In this case, there is a periodic dependence of the limiting conditional distributions on the initial point and the minimal conditional invariant distribution is a mixture, according to an exponential law, of the limiting conditional distributions.

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