6920 papers
This paper establishes an explicit second-order expansion for the volume dimension of the Julia sets of holomorphic skew products in as a perturbation parameter approaches zero, extending the classical Ruelle-McMullen results on Hausdorff dimension to non-conformal higher-dimensional dynamical systems.
This paper establishes a functional law of large numbers for a spatial model of Muller's ratchet, proving that the system converges to an infinite system of partial differential equations that rigorously determine population spreading speeds and demonstrate that deleterious mutations can indeed surf deterministic population waves.
This paper combines additive combinatorics and Diophantine geometry to establish a uniform sum-product phenomenon for one-dimensional algebraic groups over , thereby resolving Bremner's conjecture on arithmetic progressions in elliptic curve coordinates and improving upon existing results by Bays--Breuillard regarding Elekes--Szabó-type theorems.
This paper addresses the DNA coverage depth problem by developing combinatorial tools based on duality and extended weight enumerators to derive closed formulas for specific linear codes and a general expression linking coverage depth to the weight distributions of higher-field extensions.
This paper establishes that the symmetric algebra of the Bergman space on the unit disk forms a natural algebra over a square-integrable suboperad of holomorphic disk embeddings, which is identified with the affine Heisenberg vertex operator algebra and used to construct metric-dependent invariants for two-dimensional Riemannian manifolds via conformally flat factorization homology.
This paper establishes the convergence of the near-critical dimer model's height function to a massive sine-Gordon model by introducing a novel framework of discrete massive holomorphic functions with complex-valued, non-constant mass to derive exact discrete Cauchy–Riemann equations for the inverse Kasteleyn matrix.
This paper derives and analyzes a Fokker-Planck-type mean-field PDE model for stochastic reinforcement learning in market entry games, proving solution existence and demonstrating that the model captures aggregate learning and sorting phenomena with distinct time scales consistent with empirical evidence.
This paper applies the classical Lie symmetry method to a nonlinear heat-diffusion equation with variable coefficients to classify admitted symmetries, reduce the partial differential equation to ordinary differential equations, and construct invariant solutions for physically relevant cases such as Storm-type materials and power-law dependencies.
This paper establishes that embedded infinite plane triangulations within ergodic scale-free environments converge to their circle packing and Riemann uniformization embeddings on a large scale, provided that specific moment and connectivity conditions are met.
This paper presents new deformation and involutivity theorems for Poisson quasi-Nijenhuis manifolds under factorization hypotheses on their defining forms, supported by examples of involutive structures, to advance the application of this geometry to classical completely integrable systems.
This paper proposes a heuristic MIMO-CC delivery framework that enables asymmetric stream allocation while guaranteeing linear decodability through a newly derived criterion, thereby expanding the achievable Degrees of Freedom region beyond the limitations of existing symmetric-constrained designs.
This paper establishes that both geometric and homological finiteness properties of group pairs remain invariant under a suitably defined notion of quasi-isometry for group pairs.
This short note resolves a problem posed by Wickstead regarding the sequential monotone closure of spaces, a topic arising from the study of Riesz completions of regular operator spaces between Banach lattices.
This paper constructs infinitely many -component Brunnian links of 3-balls in the 4-sphere for each integer by utilizing and providing a new proof for a result concerning splitting spheres for trivial two-component links of 2-spheres.
This paper introduces and analyzes a broad class of continuous directed polymers in driven by Gaussian environments, establishing their structural properties, proving a sharp measure-theoretic dichotomy regarding their relation to Wiener measure, and demonstrating diffusive behavior in high dimensions and high temperatures, thereby extending the Alberts--Khanin--Quastel framework to higher-dimensional settings.
Inspired by R. Heitmann's proof of the Direct Summand Conjecture and G. Faltings' normalized length, this paper establishes new results on local cohomology modules in mixed characteristic using the Frobenius map, with significant implications for the study of splinters.
This paper introduces a new poset property defined via a variation of the Banach-Mazur game that strengthens -strategic closedness, proves that the Proper Forcing Axiom (PFA) is preserved under forcing with such posets, and applies this result to reproduce Magidor's theorem on the consistency of PFA with weak square principles while distinguishing the property from -operational closedness.
This paper proposes and analyzes a novel class of modified averaged vector field methods that simultaneously preserve multiple invariants for conservative Stratonovich stochastic differential equations, proving their mean square convergence order of 1 under commutative noises and demonstrating their superiority in long-time simulations through numerical experiments.
This paper establishes the probabilistic superiority of stochastic symplectic methods over non-symplectic ones by proving that the former asymptotically preserve the large deviations principles governing the exponential decay of hitting probabilities for the mean position and velocity of stochastic Hamiltonian systems, a result demonstrated via the Gärtner–Ellis theorem on the linear stochastic oscillator.
This paper determines the all-genus Hodge-Gromov-Witten theory for smooth hypersurfaces in weighted projective spaces defined by chain, loop, or general invertible polynomials, providing the first genus-zero Gromov-Witten invariants for non-Gorenstein ambient spaces where convexity fails.