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8 papers · 2 filters
On the approach to equilibrium for a polymer with adsorption and repulsion
Pietro Caputo, Fabio Martinelli, Fabio Lucio Toninelli
We consider paths of a one-dimensional simple random walk conditioned to come back to the origin after L steps (L an even integer). In the 'pinning model' each path ηhas a weight λ…
Disordered pinning models and copolymers: beyond annealed bounds
Fabio Lucio Toninelli
We consider a general model of a disordered copolymer with adsorption. This includes, as particular cases, a generalization of the copolymer at a selective interface introduced by…
The spectrum of heavy-tailed random matrices
Gerard Ben Arous, Alice Guionnet
Let be an $N\ts N$ random symmetric matrix with independent equidistributed entries. If the law of the entries has a finite second moment, it was shown by Wigner \cite{wi…
On the irrelevant disorder regime of pinning models
Giambattista Giacomin, Fabio Lucio Toninelli
Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understand…
Regularization by free additive convolution, square and rectangular cases
Serban Belinschi, Florent Benaych-Georges, Alice Guionnet
The free convolution is the binary operation on the set of probability measures on the real line which allows to deduce, from the individual spectral distributions, the spectral di…
Localization transition in disordered pinning models. Effect of randomness on the critical properties
F. Toninelli
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where f…