3 papers
math.PR2024
On the Replica Symmetry of a Variant of the Sherrington-Kirkpatrick Spin Glass
Christian Brennecke, Adrien Schertzer
We consider i.i.d. Ising spins with mean whose interactions are described by a Sherrington-Kirkpatrick Hamiltonian with a quartic correction. This model was recen…
cs.LG2024
Stochastic Differential Equations models for Least-Squares Stochastic Gradient Descent
Adrien Schertzer, Loucas Pillaud-Vivien
We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze St…
math.PR2024
Spin Covariance Fluctuations in the SK Model at High Temperature
Christian Brennecke, Adrien Schertzer, Chen Van Dam
Based on \cite{H}, it is well known that the rescaled two point correlation functions \[ \sqrt{N} \langle σ_i ; σ_j\rangle = \sqrt{N} \big( \langle σ_i σ_j\rangle -\langle σ_i\rang…