A Tale of Two Walks: Kipnis, Marchioro and Presutti Meet Kac in a Quantum World

arXiv:2609.38044 · quant-ph, cs.DS, math.PR · Submitted 2026-09-29 · Read on arXiv

quant-ph, cs.DS, math.PR

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Spectral Gap — 32× in this paper · explained in 5 episodes
• Annual Symposium on Foundations of Computer Science — 4× in this paper
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Approximate Unitary t-design — 1× in this paper · explained in 1 episode
• Approximation Bound — 1× in this paper · explained in 1 episode
• Boltzmann Equation — 1× in this paper · explained in 2 episodes

Sources

• Random unitaries from Hamiltonian dynamics
• Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs
• Random unitaries that conserve energy
• Strong random unitaries and fast scrambling

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