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Sampling the Fermi statistics and other conditional product measures

A. Gaudillière, J. Reygner (2011)

Annales de l'I.H.P. Probabilités et statistiques

Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the temperature as well as the energy values and degeneracies of the energy levels we give an explicit upper bound with leading term km ln k for the mixing time of the dynamics. We obtain such construction and upper bound as a special case of a general result on (non-homogeneous)...

Soft local times and decoupling of random interlacements

Serguei Popov, Augusto Teixeira (2015)

Journal of the European Mathematical Society

In this paper we establish a decoupling feature of the random interlacement process ℐ u ⊂ ℤ d at level u , d ≥ 3 . Roughly speaking, we show that observations of ℐ u restricted to two disjoint subsets A 1 and A 2 of ℤ d are approximately independent, once we add a sprinkling to the process ℐ u by slightly increasing the parameter u . Our results differ from previous ones in that we allow the mutual distance between the sets A 1 and A 2 to be much smaller than their diameters. We then provide an important application of this...

Sojourn time in ℤ+ for the Bernoulli random walk on ℤ

Aimé Lachal (2012)

ESAIM: Probability and Statistics

Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci. USA 35 (1949) 605–608], simpler representations may be obtained...

Sojourn time in ℤ+ for the Bernoulli random walk on ℤ

Aimé Lachal (2012)

ESAIM: Probability and Statistics

Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci....

Stability estimating in optimal stopping problem

Elena Zaitseva (2008)

Kybernetika

We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space X . It is supposed that an unknown transition probability p ( · | x ) , x ∈ X , is approximated by the transition probability p ˜ ( · | x ) , x ∈ X , and the stopping rule τ ˜ * , optimal for p ˜ , is applied to the process governed by p . We found an upper bound for the difference between the total expected cost, resulting when applying τ ˜ * , and the minimal total expected cost. The bound given is a constant times sup x ∈ X ∥ p ( · | x ) - p ˜ ( · | x ) ∥ , where ∥ · ∥ is the total variation...

Stochastic vortices in periodically reclassified populations

Gracinda Rita Guerreiro, João Tiago Mexia (2008)

Discussiones Mathematicae Probability and Statistics

Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations...

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