arXiv subjects

Sotirios Kotitsas

Publications and source records attributed to Sotirios Kotitsas.

3 recordsLinked to original sources

arXiv2026

Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle

We consider the infinite-width limit of a fully connected deep neural network with general weights, and we prove quantitative general bounds on the $2$-Wasserstein distance between the network and its infinite-width Gaussian limit, under appropriate regularity assumptions on the activation function. Our main tool is a Lindeberg principle for Deep Neural Networks, which we use to successively replace the weights on each layer by Gaussian random variables.

math.PR↗

arXiv2025

Edwards-Wilkinson limit for a stochastic advection-diffusion PDE

We consider a diffusion in a Gaussian random environment that is white in time and study the large-scale behavior of the quenched density with respect to the Lebesgue measure. We show that under diffusive rescaling, the fluctuations of the density converge to a Gaussian limit, described by an additive stochastic heat equation. In the case where the environment is divergence-free, our result can be interpreted as computing the scaling limit of the first-order correction to the quenched Central Limit Theorem.

math.PR↗

arXiv2025

The heat equation with time-correlated random potential in d=2: Edwards-Wilkinson fluctuations

We consider the stochastic PDE: $\partial_tu(t,x)=\frac{1}{2}Δu(t,x)+β{}u(t,x)V(t,x),$ in dimension $d=2$, where the potential V is the space and time mollification of the two-dimensional space-time white noise. We show that after renormalizing, the fluctuations of the solution converge to the Edwards-Wilkinson limit with an explicit effective variance and constant effective diffusivity. Our main tool is a Markov chain on the space of paths which we use to establish an extension of the Kallianpur-Robbins law to a specific regenerative process.

math.PR↗