Establishes discrete log-concavity of ground states for convex potentials and extends Reichardt's HWS tunneling analysis to quadratic spikes via new spectral gap bounds.
Poisson Process Approximations for the Ewens Sampling Formula
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Introduces a novel exclusion process with mass and energy conservation and proves convergence of fluctuation fields to uncoupled stochastic Burgers equations for suitable parameters.
For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
Transpose-invariant spectral diagnostics on attention operators are orientation-blind, and a φ-G two-axis diagnostic distinguishes hallucination modes with 0.62-0.84 LC-AUROC and predicted polarity reversal.
Develops a constrained optimization framework for position-independent irreversible perturbations of ULA that yields an explicit optimal design accounting for both spectral-gap mixing and weighted jump-distance bias.
The singular-value gap of a nonreversible Markov generator bounds finite-time variance of empirical averages uniformly over L2 functions and implies solvability of the Poisson equation when positive.
The historical sequence of papal names is consistent with a random-copying process with innovation, as predicted by Ewens sampling theory and the Chinese restaurant process.
In finite-depth random linear optical circuits, entanglement grows at most diffusively and robust circuit complexity scales similarly, with depth bounds ensuring near-maximal subsystem entanglement and closeness to Haar unitaries.
Presents Block-Shifted CR algorithm using SVD and deflation to extend convergence of cyclic reduction for quadratic matrix equations with multiple unit-circle eigenvalues.
Four controlled identical realizations of a galaxy-cluster zoom-in simulation reveal 10-25% variability in galaxy masses driven by stochastic processes and modulated by feedback, establishing a noise-dominated but statistically reproducible regime at low resolution.
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