Dima Ioffe, Senya Shlosman, Yvan Velenik
We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular interactions with continuous symmetry, when the symmetry is broken in the thermodynamic limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of $k$-integrable parametrized measure models, we extend the Cramér-Rao inequality to $2$-integrable (possibly singular) statistical models for general $φ$-estimations, where $φ$ is a $V$-valued feature function and $V$ is a topological vector space. Thus we derive an intrinsic Cramér-Rao inequality in the most general terms of parametric statistics.
We study the limiting behavior of the two-dimensional singular stochastic stochastic cubic nonlinear complex Ginzburg-Landau with Gibbs measure initial data. We show that in the appropriate small viscosity and small noise regimes, the limiting dynamics is given by the deterministic cubic nonlinear Schrödinger equation at Gibbs equilibrium. In order to obtain this convergence, our approach combines both heat and Schrödinger analysis, within the framework of the Fourier restriction norm method of Bourgain (1993).
This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cram{é}r-Lundberg claims, by allowing singular dividend payments and capital injections. Using variational techniques and embedding the trajectories in an appropriate family of occupation measures, we provide the linearisation of such problems in which the continuous control is given by reinsurance policies and the singular one by dividends and capital injections. The linearisation …
We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and Hölder continuous drift has a Hölder continuous density function. This result complements recent results of Fournier-Printems \cite{F1}, where the density is shown to exist if both coefficients are Hölder continuous and exemplifies the role of the drift coefficient in the regularity of the density of a diffusion.
The class $\boldsymbol{Q}$ and mixture distributions with dominated continuous singular parts
研究分布函数类 $\oldsymbol{Q}$ 在连续奇异部分受离散部分控制时的归属条件，提出拟无穷可分判据，推广已有结果并解决了相关分解问题。
We study asymptotic behavior of conditional least squares estimators for critical continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.
We study asymptotic behavior of conditional least squares estimators for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.
The Milstein scheme for singular SDEs with Hölder continuous drift
针对仅具Hölder连续漂移项的奇异SDE，研究Milstein格式的$L^p$收敛速率，借助噪声正则化尤其是随机缝合法，在扩散项椭圆且正则时得到与加性噪声情形一致的速率，其所需的格式分布精确估计也具独立价值。
Conditions are established under which the optimal control of processes having both absolutely continuous and singular (with respect to time) controls are equivalent to linear programs over a space of measures on the state and control spaces. This paper considers long-term average and discounted criteria and includes budget and resource constraints. The linear programs optimize over measures representing the expected occupation measure of the state and absolutely continuous control processes and a similar expected occupation measure of the state and control when the singular action of the proc…
We consider the singular boundary-value problem Δu = f(u) in D; u|_dD= phi, where 1. D is a bounded C^2-domain of R^d, d >= 3 2. f: (0,1) -> (0,1) is a locally Hölder continuous function such that f(u) -> 1 as u -> 0 at the rate u^{-α}, for some αin (0,1), 3. and phi is a positive continuous function satisfying certain growth assumptions. We show existence of solutions bounded below by a positive harmonic function, which are smooth in D and continuous in D-bar. Such solutions are shown to satisfy a boundary Harnack principle. Probabilistic techniques are used in proving the main results.
The well-posedness and regularity estimates in initial distributions are derived for singular McKean-Vlasov SDEs, where the drift contains a locally standard integrable term and a superlinear term in the spatial variable, and is Lipchitz continuous in the distribution variable with respect to a weighted variation distance. When the superlinear term is strengthened to be Lipschitz continuous, Wangs Harnack inequality is established. These results are new also for the classical Ito SDEs where the coefficients are distribution independent.
We consider the system of stochastic differential equations dX_t=A(X_{t-}) dZ_t, where Z_t^1, ..., Z^d_t are independent one-dimensional symmetric stable processes of order α, and the matrix-valued function A is bounded, continuous and everywhere non-degenerate. We show that bounded harmonic functions associated with X are Holder continuous, but a Harnack inequality need not hold. The Levy measure associated with the vector-valued process Z is highly singular.
Approximation of Singular-Stopping Control Driven by Hawkes Processes via Rescaled MDPs
本文通过重新缩放的马尔可夫决策过程近似由Hawkes过程驱动的奇异停止控制问题，并展示了其在电力投资中的应用。
Suppose $X$ is an $N \times n$ complex matrix whose entries are centered, independent, and identically distributed random variables with variance $1/n$ and whose fourth moment is of order ${\mathcal O}(n^{-2})$. In the first part of the paper, we consider the non-Hermitian matrix $X A X^* - z$, where $A$ is a deterministic matrix whose smallest and largest singular values are bounded below and above respectively, and $z\neq 0$ is a complex number. Asymptotic probability bounds for the smallest singular value of this model are obtained in the large dimensional regime where $N$ and $n$ diverge t…
Path independence for the additive functionals of stochastic Volterra equations with singular kernels and Hölder continuous coefficients
本文针对奇异核、Hölder 连续系数随机 Volterra 方程，先证明适定性，再借助抛物型 SPDE 的 mild 表述与随机发展方程结果刻画可加泛函路径无关性，并应用于分数 Brown 运动相关核。
Time-inconsistent singular control problems: Reflection and Absolutely continuous controls with exploding rates
本文研究非指数贴现导致的时间不一致奇异控制问题，提出涵盖传统反射控制与速率爆炸的温和阈值控制的新控制类，建立基于变分不等式的验证定理，并在库存管理案例中首次构造出具有不可达边界的均衡解。
In this work we consider the Anderson model on the $d$-dimensional lattice with the single site potential having singular distribution, mainly $α$-Hölder continuous ones and show that the eigenvalue statistics is Poisson in the region of exponential localization.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。