7 papers
Digit Mixing under Polynomial Maps
Chokri Manai
Let be a random number where we model the digits as independent Bernoulli random variables with possibly non-identical parameters $p_n=\mathbb{P…
The quantum Almeida-Thouless line in the self-overlap-corrected quantum Sherrington-Kirkpatrick model
Chokri Manai, Simone Warzel
We present a complete analysis of the glass transition in the self-overlap-corrected Sherrington-Kirkpatrick (SK) model in a transverse magnetic field, also referred to as the quan…
Super-Dense Sets and Their Role in the Theory of Normal Numbers
Chokri Manai
We introduce and study a new topological notion of the size for subsets of the real line, called \emph{super-density}. A set is super-dense if for every non-em…
The Quantum Random Energy Model is the Limit of Quantum -Spin Glasses
Anouar Kouraich, Chokri Manai, Simone Warzel
We consider the free energy of a class of spin glass models with -spin interactions in a transverse magnetic field. As , the infinite system-size free energy is…
Quantum Mean-Fields Spin Systems in a Random External Field
Chokri Manai
In this work, we consider general exchangeable quantum mean-field Hamiltonian such as the prominent quantum Curie-Weiss model under the influence of a random external field. Despit…
Transcendence Meets Normality: Construction of Transcendentally Normal Numbers
Chokri Manai
In this work, we study real numbers for which is (absolutely) normal for every non-constant integer-valued polynomial . We call such numbers transcendentally normal.…