274 papers
This paper establishes the local well-posedness of the generalized parabolic Anderson model and the -equation on the two-dimensional torus with random, noise-correlated coefficients by proving that naive renormalisation fails due to variance blow-up and instead demonstrating convergence through the use of random renormalisation functions supported by novel stochastic estimates.
This paper establishes the global-in-time well-posedness of stochastic third-grade fluid equations on a two-dimensional torus with additive noise and proves the existence, uniqueness, and first-order optimality conditions for a velocity tracking control problem by transforming the system into an equivalent pathwise deterministic one.
This paper investigates the limit shapes and fluctuations of random Young diagrams arising from symplectic group duality by deriving semiclassical orthogonal polynomials via Christoffel transformation from Krawtchouk polynomials and analyzing their asymptotic behavior through an integral representation, thereby overcoming the lack of a free-fermionic representation available in the general linear case.
This paper proves that the infinite system-size free energy of quantum -spin glasses in a transverse magnetic field converges to that of the quantum random energy model as , achieved by combining non-commutative analytical techniques with the geometry of extreme negative deviations in classical -spin glasses.
This paper establishes an exact recursive equation for the covariation measures of the two-dimensional stochastic heat equation at criticality, explicitly expressing the quadratic variations of its martingale parts in terms of the equation's solutions and two-body delta-Bose gas semigroups through asymptotic analysis and new fourth-order moment bounds.
This paper establishes a unified framework for proving the almost everywhere pointwise convergence of sparse ergodic averages in for both deterministic and random sequences within specific parameter ranges, while providing new quantitative convergence estimates that improve upon previous non-quantitative results.
This paper introduces a novel transformation-based, doubly-adaptive quasi-Milstein scheme for jump-diffusion SDEs with discontinuous drift and degenerate diffusion, achieving a strong convergence rate of order 1 in under assumptions weaker than those in existing literature.
This paper establishes the stability and uniqueness of a stochastic branching algorithm for solving semilinear heat equations by deriving sufficient criteria for the integrability of random functionals to prevent solution explosion.
This paper introduces new classes of multivariate heavy-tailed distributions based on the single big jump principle, investigates their closure properties and asymptotic behaviors under various operations, and applies these findings to evaluate the present value of total claims in a risk model with dependent financial factors.
This paper establishes two weak formulations for the supercooled Stefan problem with transport noise, providing a probabilistic representation via a conditional McKean--Vlasov problem that characterizes finite-time blow-ups and continuous evolution based on initial conditions, while identifying a minimal solution that resolves instabilities through jump discontinuities.
This paper develops an asymptotic expansion formula for bootstrap coverage probabilities in high dimensions to theoretically explain why third-moment matching wild bootstrap methods outperform normal approximations, demonstrating that such methods achieve second-order accuracy without studentization under specific covariance structures or via a double wild bootstrap approach.
This paper demonstrates that the occupation measure of planar Brownian motion exhibits a constant height gap of $5/\pi$ across its outer boundary, a result derived by leveraging the expected area of the domain delimited by a Brownian bridge and drawing parallels to height gap properties in the Gaussian free field and Brownian loop soup.
This paper establishes the convergence of the expected signature of a generalized physical Brownian motion to a nontrivial tensor in the small mass limit () by analyzing a graded PDE system, revealing that the limit differs from the standard mathematical Brownian motion and exhibits explicit combinatorial patterns when the system's coefficient matrix is diagonalizable.
This paper characterizes the amenability of countable Borel equivalence relations via the uniform Liouville property, investigates Kesten's property for return probabilities on topological groups, and constructs an amenable contractible Polish group lacking this property by linking it to anti-concentration inequalities in measurable lamplighter groups.
This paper introduces dilated seminorm-enriched category theory as a unifying framework for central limit theorems, establishing an abstract CLT that recovers classical results and yields novel applications in symplectic manifolds and statistical mechanics.
This paper establishes that Metropolis–Hastings algorithms with non-geometrically ergodic proposals and high acceptance rates at large states fail to be geometrically ergodic, while further demonstrating that guided walk variants converge twice as fast as random walk versions for polynomial-tailed targets but exhibit similar ballistic speeds to random walks for strictly convex potentials.
This paper derives an explicit Laplace-type asymptotic approximation with vanishing relative error for the tail probability of the product of independent Poisson random variables, utilizing Stirling's approximation, a constrained saddle-point method, and the Lambert function.
Motivated by Pitman and Yor's construction of the 3-dimensional Bessel process, this paper demonstrates that applying a similar excision procedure to a Brownian bridge yields a 3-dimensional Bessel bridge.
This paper derives explicit asymptotic approximations for the right-tail probability of the product of independent normal random variables as the threshold tends to infinity, utilizing a boundary saddle-point method to establish formulas with relative error $1+O(x^{-1/n})$ that account for nonzero means and admissible sign patterns.
This paper establishes that for Bayesian inference of planted matchings between correlated 1D point sets under critical scaling, the posterior distribution admits a local approximation with a well-defined infinite-volume limit in the partial matching case, whereas the exact matching case requires global sorting and a flow-based indexing to define its asymptotic marginal statistics.