On the Real Reliability Roots of Graphs
This paper investigates the real roots of graph reliability polynomials, proving that almost every graph possesses a nonreal reliability root and that these polynomials have roots dense on the interval where .
🔢 Category
math.PR
271 papers
Critical stationary fluctuations in reaction--diffusion processes
This paper establishes that for a one-dimensional reaction-diffusion process combining symmetric simple exclusion and critical Glauber dynamics, the rescaled total magnetization converges to a non-Gaussian distribution with a quartic-exponential density, while the density field's fluctuations on zero-mean modes vanish, indicating that the macroscopic behavior is dominated by the magnetization mode.
Uniform Lorden-type bounds for overshoot moments for standard exponential families: small drift and an exponential correction
This paper establishes uniform Lorden-type moment bounds for the overshoot of random walks with sign-changing increments from standard exponential families in the small-drift regime, demonstrating that these bounds improve to a constant of 1 for large barriers and providing explicit exponential convergence rates interpreted through optimal transport metrics.
On the structure of the Poisson trinomial distribution
This paper analyzes the structure of the Poisson trinomial distribution by demonstrating that its probability mass function decomposes into two interleaved, normalized Poisson binomial distributions supported on integers and half-integers, respectively, and establishes bounds on the proximity of their conditional means and modes to the unconditional mean.
On the statistics of random-to-top shuffles
This paper establishes limit theorems for the number of fixed points, descents, and inversions in iterated random-to-top shuffles by employing analytical methods and novel combinatorial decompositions, thereby resolving open questions posed by Diaconis, Fulman, and Pehlivan.
Strong convergence of finite element approximations for a fourth-order stochastic pseudo-parabolic equation with additive noise
This paper establishes strong convergence rates for semi-discrete and fully discrete finite element approximations of a fourth-order stochastic pseudo-parabolic equation driven by additive noise, supported by numerical experiments.
Isoperimetric inequality for nonlocal bi-axial discrete perimeter
This paper solves a novel nonlocal discrete isoperimetric problem by characterizing the minimizers of a generalized "bi-axial" perimeter that accounts for all internal and external components of a polyomino, thereby establishing a rigorous link to the metastable behavior of a long-range bi-axial Ising model.
Small noise asymptotics for a class of jump-diffusions with heavy tails for large times
This paper establishes that for positive recurrent Lévy diffusions driven by scaled Brownian motion and -stable processes ($1<\alpha<2$) in the small noise regime, the large-time limiting behavior of the one-dimensional marginal distribution is determined by the optimal value of a deterministic control problem featuring both continuous and impulse controls.
Concentration Inequalities for Sub-Weibull Random Tensors
This paper extends concentration inequality theory to simple random tensors with heavy-tailed sub-Weibull coefficients by establishing bounds that reveal a phase transition between sub-Gaussian and heavy-tailed regimes, utilizing a new Generalized Maximal Inequality and Nagaev-type martingale analysis.
Fine asymptotics of the magnetization of the annealed dilute Curie-Weiss model
This paper establishes sharp cumulant bounds for the magnetization in the annealed dilute Curie-Weiss model under high-temperature conditions with an external magnetic field, thereby proving a central limit theorem with convergence rates, a moderate deviation principle, concentration inequalities, and mod-Gaussian convergence for the regime where .
Diversification and Stochastic Dominance: When All Eggs Are Better Put in One Basket
This paper challenges the conventional wisdom that diversification always reduces risk by demonstrating that for heavy-tailed losses with infinite means, a diversified portfolio can stochastically dominate a "one-basket" benchmark, thereby increasing the probability of exceeding any given loss threshold.
A stochastic Gordon-Loeb model for optimal cybersecurity investment under clustered attacks
This paper proposes a continuous-time stochastic extension of the Gordon-Loeb model that incorporates Hawkes processes to capture attack clustering, demonstrating through dynamic programming that accounting for such clustering yields more responsive and effective cybersecurity investment policies compared to traditional static or Poisson-based approaches.
Sampling on Discrete Spaces with Temporal Point Processes
This paper introduces a novel sampling framework using multivariate temporal point processes modeled as coupled infinite-server queues to efficiently sample from discrete distributions with downward-closed support, demonstrating superior performance over existing birth-death and Zanella processes while enabling biologically plausible recurrent neural network applications.
A Dynamical Approach to Non-Extensive Thermodynamics
This paper develops a non-extensive thermodynamic formalism for one-sided shifts by introducing -entropy and -pressure concepts, proving the existence and uniqueness of -equilibrium states for Lipschitz potentials, and establishing connections between these generalized structures and classical Ruelle transfer operators.
Geometric early warning indicator from stochastic separatrix structure in a random two-state ecosystem model
This paper proposes a robust geometric early warning indicator based on the width of the stochastic separatrix in a two-state ecosystem model, which successfully predicts rapid under-ice phytoplankton blooms in the Arctic where conventional critical slowing down signals fail due to strong noise or limited data.
Polynomially Over-Parameterized Convolutional Neural Networks Contain Structured Strong Winning Lottery Tickets
This paper proves that randomly initialized, polynomially over-parameterized convolutional neural networks contain structured subnetworks capable of approximating smaller networks without training, by developing new mathematical tools to overcome previous limitations in analyzing the Strong Lottery Ticket Hypothesis for structured pruning.
Global universality via discrete-time signatures
This paper establishes global universal approximation theorems for path-dependent functionals on spaces of piecewise linear paths using linear functionals of discrete-time signatures, demonstrating their applicability to Brownian motion-driven systems such as random and stochastic ordinary differential equations.
A Gaussian Comparison Theorem for Training Dynamics in Machine Learning
This paper establishes a non-asymptotic Gaussian comparison theorem based on Gordon's theorem to rigorously validate dynamic mean-field expressions and derive refined iterative approximations for the training dynamics of machine learning models, such as perceptrons, under Gaussian mixture data.
Jensen's inequality for partial traces in von Neumann algebras
Motivated by recent finite-dimensional results, this paper establishes Jensen's inequality for partial traces within both semifinite and general non-tracial von Neumann algebras.
Non-standard analysis for coherent risk estimation: hyperfinite representations, discrete Kusuoka formulae, and plug-in asymptotics
This paper establishes a non-standard analysis framework that unifies coherent risk measures and their finite-sample estimators through hyperfinite representations, yielding discrete Kusuoka formulae, plug-in consistency results, and asymptotic normality via a transparent probability-to-statistics dictionary.