I will discuss the limiting distribution of quadratic Weyl sums and their generalisations (e.g. classical Jacobi theta functions). Quadratic Weyl sums are a special kind of exponential sums that appear naturally in number theory, mathematical physics, and representation theory. They can be interpreted as deterministic walks (with a random ‘seed’) in the complex plane. Generalising Sarnak’s equidistribution of horocycles under the action of the geodesic flow, one can study the limiting distribution of such Weyl sums. A stochastic process of number-theoretical origin can be defined using such sums. ------- Seminario nell'ambito del corso di dottorato "Randomness in Number Theory: dynamical and probabilistic methods”, tenuto dal Prof. Cellarosi per il Dottorato in Matematica Unibo