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21 papers · 2 filters
Number of relevant directions in Principal Component Analysis and Wishart random matrices
Satya N. Majumdar, Pierpaolo Vivo
We compute analytically, for large , the probability that a Wishart random matrix has eigenvalues exceeding a threshold , including it…
Universal Order Statistics of Random Walks
Gregory Schehr, Satya N. Majumdar
We study analytically the order statistics of a time series generated by the successive positions of a symmetric random walk of n steps with step lengths of finite variance σ^2. We…
Wigner-Crystal Formulation of Strong-Coupling Theory for Counter-ions Near Planar Charged Interfaces
L. Šamaj, E. Trizac
We present a new analytical approach to the strong electrostatic coupling regime (SC), that can be achieved equivalently at low temperatures, high charges, low dielectric permittiv…
Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit
Philippe Mounaix, Satya N. Majumdar, Abhimanyu Banerjee
We derive the criterion for the Bose-Einstein condensation (BEC) of a Gaussian field (real or complex) in the thermodynamic limit. The field is characterized by its covariance…
Lévy flights on the half line
Reinaldo Garcia-Garcia, Alberto Rosso, Gregory Schehr
We study the probability distribution function (pdf) of the position of a Lévy flight of index 0<α<2 in presence of an absorbing wall at the origin. The solution of the associated…
Field Theory of Fluctuations in Glasses
Silvio Franz, Giorgio Parisi, Federico Ricci-Tersenghi +1
We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium argu…