An exponential rate of convergence for a class of boltzmann processes

Some new results on information percolation

“…This proves the first assertion. A similar calculation to the proof of Lemma 3 in Ferland and Giroux [10] gives us the second result.…”

“…In Ferland and Giroux [10] the authors study a class of kinetic equations of Kac's type and they show, for binary collisions, a convergence to the steady state at an exponential rate. The convergence in Ferland and Giroux [10] is obtained along a set of convenient test functions with a telescoping technique due to Trotter [15] and with the use of a version of Wild sums obtained from judicious conditioning. We extend the results of Ferland and Giroux [10] for any m ≥ 2.…”

“…The convergence in Ferland and Giroux [10] is obtained along a set of convenient test functions with a telescoping technique due to Trotter [15] and with the use of a version of Wild sums obtained from judicious conditioning. We extend the results of Ferland and Giroux [10] for any m ≥ 2.…”

“…We have that e n ≤ cn a−1 where a = 1−η m−1 and η is such that 1 − η = E m i=1 H 2 i by Lemma 5 below. Then proceeding as in Theorem 3 of Ferland and Giroux [10] with the extended Wild sum and replacing 1 − η by…”

Information Percolation: Some General Cases with an Application to Econophysics

“…If we decompose A n in its m subtrees from its first node we can apply a similar reasoning to Ferland-Giroux (1991) in order to obtain that e n ≤ cn a−1 where a = 1−η m−1 and η is such that 1…”