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math.PR2026
Heat flow and repeated differentiation of polynomials with i.i.d. roots
Jonas Jalowy
How do the zeros of a polynomial evolve under the holomorphic heat flow or repeated differentiation? In this work, we develop a unified probabilistic proof to three conjectures on…
math.PR2026
Pólya--Schur problems and free probability
Andrew Campbell, Jonas Jalowy
In this work, we build a bridge between the Pólya--Schur program and Voiculescu's free probability theory. A cornerstone of the former is the Pólya--Benz Theorem, classifying a cen…
math.PR2026
The infinite block spin Ising model
Jonas Jalowy, Isabel Lammers, Matthias Löwe
We study a block mean-field Ising model with spins split into blocks, with Curie-Weiss interaction within blocks and nearest-neighbor coupling between blocks. While previ…