Véronique Gayrard
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Véronique Gayrard has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Anton Bovier
Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany
5 shared publications - Gérard Ben Arous
Courant Institute of Mathematical Sciences, New York University, New York, USA
2 shared publications - Markus Klein
Institut für Mathematik, Universität Potsdam, Potsdam, Germany
2 shared publications - M. Eckhoff
Institut für Mathematik Universität Potsdam Am Neuen Palais 10 D-14469 Potsdam Germany
1 shared publication - M. Klein
Institut für Mathematik Universität Potsdam Am Neuen Palais 10 D-14469 Potsdam Germany
1 shared publication - Michael Eckhoff
Universität Zürich, Switzerland
1 shared publication
Latest Publications
- 1 May 2003
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 236 (1) , 1-54
Glauber Dynamics of the Random Energy Model
- 1 May 2003
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 236 (1) , 1-54
Glauber Dynamics of the Random Energy Model
- 1 April 2003
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 235 (3) , 379-425
Glauber Dynamics of the Random Energy Model
- 1 April 2003
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 235 (3) , 379-425
Glauber Dynamics of the Random Energy Model
- 9 November 2000
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 33 (46) , L447-L451
Metastability and small eigenvalues in Markov chains
In this Letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerably greater precision than has so far been available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state and sharp estimates of the convergence of the probability distribution of the metastable transition times to the exponential distribution.
- 9 November 2000
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 33 (46) , L447-L451
Metastability and small eigenvalues in Markov chains
In this Letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerably greater precision than has so far been available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state and sharp estimates of the convergence of the probability distribution of the metastable transition times to the exponential distribution.
- Open Access
Metastability and low lying spectra in reversible Markov chains
We study a large class of reversible Markov chains with discrete state space and transition matrix $P_N$. We define the notion of a set of {\it metastable points} as a subset of the state space $\G_N$ such that (i) this set is reached from any point $x\in \G_N$ without return to x with probability at least $b_N$, while (ii) for any two point x,y in the metastable set, the probability $T^{-1}_{x,y}$ to reach y from x without return to x is smaller than $a_N^{-1}\ll b_N$. Under some additional non-degeneracy assumption, we show that in such a situation: \item{(i)} To each metastable point corresponds a metastable state, whose mean exit time can be computed precisely. \item{(ii)} To each metastable point corresponds one simple eigenvalue of $1-P_N$ which is essentially equal to the inverse mean exit time from this state. The corresponding eigenfunctions are close to the indicator function of the support of the metastable state. Moreover, these results imply very sharp uniform control of the deviation of the probability distribution of metastable exit times from the exponential distribution.Open AccessMetastability and low lying spectra in reversible Markov chains
We study a large class of reversible Markov chains with discrete state space and transition matrix $P_N$. We define the notion of a set of {\it metastable points} as a subset of the state space $\G_N$ such that (i) this set is reached from any point $x\in \G_N$ without return to x with probability at least $b_N$, while (ii) for any two point x,y in the metastable set, the probability $T^{-1}_{x,y}$ to reach y from x without return to x is smaller than $a_N^{-1}\ll b_N$. Under some additional non-degeneracy assumption, we show that in such a situation: \item{(i)} To each metastable point corresponds a metastable state, whose mean exit time can be computed precisely. \item{(ii)} To each metastable point corresponds one simple eigenvalue of $1-P_N$ which is essentially equal to the inverse mean exit time from this state. The corresponding eigenfunctions are close to the indicator function of the support of the metastable state. Moreover, these results imply very sharp uniform control of the deviation of the probability distribution of metastable exit times from the exponential distribution. - Open Access
Metastability and small eigenvalues in Markov chains
In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.
Open AccessMetastability and small eigenvalues in Markov chains
In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.