Anne Fey
Delft University of Technology
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Publication
Featured researches published by Anne Fey.
Annals of Probability | 2009
Anne Fey; Ronald Meester; Frank Redig
We study the sandpile model in infinite volume on Z d . In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure μ, are μ-almost surely stabilizable. We prove that stabilizability does not depend on the particular procedure of stabilization we adopt. In d = 1 and μ a product measure with density ρ = 1 (the known critical value for stabilizability in d = 1) with a positive density of empty sites, we prove that μ is not stabilizable. Furthermore, we study, for values of p such that μ is stabilizable, percolation of toppled sites. We find that for p > 0 small enough, there is a subcritical regime where the distribution of a cluster of toppled sites has an exponential tail, as is the case in the subcritical regime for ordinary percolation.
Physical Review Letters | 2010
Anne Fey; Lionel Levine; David B. Wilson
A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the Abelian sandpile model equals the threshold density of the fixed-energy sandpile. We refute this prediction for a wide variety of underlying graphs, including the square grid. Driven dissipative sandpiles continue to evolve even after reaching criticality. This result casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the Abelian sandpile model at stationarity.
Advances in Applied Probability | 2008
Anne Fey; Remco van der Hofstad; Mj Klok
We study sample covariance matrices of the form W = (1 / n) C C T, where C is a k x n matrix with independent and identically distributed (i.i.d.) mean 0 entries. This is a generalization of the so-called Wishart matrices, where the entries of C are i.i.d. standard normal random variables. Such matrices arise in statistics as sample covariance matrices, and the high-dimensional case, when k is large, arises in the analysis of DNA experiments. We investigate the large deviation properties of the largest and smallest eigenvalues of W when either k is fixed and n → ∞ or k n → ∞ with k n = o(n / log log n), in the case where the squares of the i.i.d. entries have finite exponential moments. Previous results, proving almost sure limits of the eigenvalues, require only finite fourth moments. Our most explicit results for large k are for the case where the entries of C are ∓ 1 with equal probability. We relate the large deviation rate functions of the smallest and largest eigenvalues to the rate functions for i.i.d. standard normal entries of C . This case is of particular interest since it is related to the problem of decoding of a signal in a code-division multiple-access (CDMA) system arising in mobile communication systems. In this example, k is the number of users in the system and n is the length of the coding sequence of each of the users. Each user transmits at the same time and uses the same frequency; the codes are used to distinguish the signals of the separate users. The results imply large deviation bounds for the probability of a bit error due to the interference of the various users.
Journal of Statistical Physics | 2012
Aernout C. D. van Enter; Anne Fey
In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally determined by the ‘easiest growth direction’ in the model. In contrast to anisotropic bootstrap percolation in two dimensions, in three dimensions the order of the metastability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation.
Journal of Statistical Physics | 2010
Anne Fey; Lionel Levine; Yuval Peres
Physical Review E | 2010
Anne Fey; Lionel Levine; David B. Wilson
Markov Processes and Related Fields | 2015
Anne Fey; Ronald Meester
Journal of Hydraulic Engineering | 2012
Aernout C. D. van Enter; Anne Fey
Journal of Cellular Automata | 2010
F. Michel Dekking; Leonard van Driel; Anne Fey
DCC | 2005
Anne Fey; Fhj Redig