The symmetric Dyson exclusion process exhibits ballistic scaling and non-local hydrodynamics with current j[ρ] = (1/π) sin(πρ) sinh(π H ρ) where H is the Hilbert transform, equivalent to a local two-field system, with exact solutions for block initial states matching simulations.
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Eigenvalues of Haar-random matrices over Z_p are asymptotically evenly distributed among algebraic extensions of Q_p by degree, with all but a bounded expected number lying in the maximal unramified extension Q_p^un; analogous results hold for roots of random Haar polynomials over Z_p.
A Feynman-Kac formula is proved for the ultraviolet-renormalized spin-boson model, showing that ground state existence for infrared-regular versions survives removal of the ultraviolet cutoff.
citing papers explorer
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Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions
The symmetric Dyson exclusion process exhibits ballistic scaling and non-local hydrodynamics with current j[ρ] = (1/π) sin(πρ) sinh(π H ρ) where H is the Hilbert transform, equivalent to a local two-field system, with exact solutions for block initial states matching simulations.
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Eigenvalue Distribution of $p$-adic Random Matrices Among Algebraic Extensions, with an Analogue for $p$-adic Random Polynomials
Eigenvalues of Haar-random matrices over Z_p are asymptotically evenly distributed among algebraic extensions of Q_p by degree, with all but a bounded expected number lying in the maximal unramified extension Q_p^un; analogous results hold for roots of random Haar polynomials over Z_p.
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A Feynman-Kac Formula for the Subcritical Ultraviolet-Renormalized Spin Boson Model
A Feynman-Kac formula is proved for the ultraviolet-renormalized spin-boson model, showing that ground state existence for infrared-regular versions survives removal of the ultraviolet cutoff.