Daniel Heydecker

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20242026

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math.PR2026

Pathological Large Deviations of the KMP Process in Dimension $d \geq 2$

Daniel Heydecker

We study dynamic large deviations for the Kipnis--Marchioro--Presutti process on the discrete torus $T_{N}^{d}$ . By recasting the candidate rate function in terms of a linear…

math.PR2026

The Porous Medium Equation: Multiscale Integrability in Large Deviations

Benjamin Gess, Daniel Heydecker

We consider a zero-range process $I^\cdot_{t}^{N} (x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t…

math.PR2025

Matching Large Deviation Bounds of the Zero-Range Process in the whole space

Benjamin Fehrman, Benjamin Gess, Daniel Heydecker

We consider the large deviations of the hydrodynamic rescaling of the zero-range process on $Z^{d}$ in any dimension $d \geq 1$ . Under mild and canonical hypotheses on the loc…

math.PR2024

Large time analysis of the rate function associated to the Boltzmann equation: dynamical phase transitions

Giada Basile, Dario Benedetto, Lorenzo Bertini +1

We analyse the large time behaviour of the rate function that describes the probability of large fluctuations of an underlying microscopic model associated to the homogeneous Boltz…

Pathological Large Deviations of the KMP Process in Dimension d≥2

The Porous Medium Equation: Multiscale Integrability in Large Deviations

Matching Large Deviation Bounds of the Zero-Range Process in the whole space

Large time analysis of the rate function associated to the Boltzmann equation: dynamical phase transitions

Pathological Large Deviations of the KMP Process in Dimension $d \geq 2$