Martina Dal Borgo, Emma Hovhannisyan, Alain Rouault
We extend recent results on the Asymptotic Equipartition Property for the density of $n$ particles in $β$-ensembles, as $n$ tends to infinity. We prove the Large Deviation Principle of the log-density for a general potential and the mod-gaussian convergence in the classical examples.
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
Asymptotic spectral independence of Wigner ensembles
我们考虑由宏观距离分开的维格纳系综的本征值簇的联合分布（即，在与椭圆定律的边缘之间的差相同的尺度上）。我们证明了在平均条件下，任何有限簇集合的相关函数收敛于独立点过程的相关函数。这个证明在很大程度上依赖于Erdos、Ramirez、Schlein和Yau开发的机器。
Pathwise asymptotic behavior of random determinants in the uniform Gram and Wishart ensembles
本文研究了一类随机对称矩阵行列式的渐近性质。若B_{n,r}是n × r的矩形矩阵，B_{n,r} '是它的转置矩阵，当n，r趋于无穷大时，研究了det（B_{n,r} ' B_{n,r}），r/n \to c \in（0，1）. B_{n,r}的r个列向量是独立选择的，具有共同的分布ν_n。Wishart系综对应于标准正态分布ν_n = { \cal N}（0，I_n）。我们把单位球面上的均匀分布ν_n = σ_n所对应的系综称为均匀Gram系综。在Wishart系综中，众所周知的Bartlett定理将上述行列式分解为卡方变量的乘积。这同样适用于统一的格拉姆合奏。这使我们能够研究过程\{ \frac{1}{n} \log \det \big（B_{n,\lfloor nt\rfloor} ' B_{n,\lfloor nt\rfloor} \big），t \in [0，1]\}及其作为n \to \infty的渐近行为：a.s.收敛、波动、大偏差。我们将边际（固定t）的结果与谱方法得到的结果联系起来。
We investigate $β$-Generalized random Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We investigate general method names as equilibrium measure method. When taking $n$ large limit we will see that the asymptotic density of eigenvalues generalize the Wigner semi-circle law.
Some asymptotic properties of the spectrum of the Jacobi ensemble
对于密度对应于Jacobi系综$$c \cdot \prod_{i < j} | λ_i - λ_j |^β\prod^n_{i=1} (2 - λ_i)^a (2 + λ_i)^b I_{(-2,2)} (λ_i) $$ $(a, b > -1, β> 0) $的随机本征值，如果参数$a, b,$ $β$依赖于$n$和$n \to \infty$，则导出了Jacobi多项式根的强一致逼近.粗略地说，特征值可以用参数为$((2a+2)/β-1, (2b+2)/β-1)$的Jacobi多项式的根一致地近似，其中误差为$\{\log n/(a+b) \}^{1/4}$阶。当$n \to \infty$及参数$a, b$和$β$随$n$变化时，这些结果被用来研究相应谱分布的渐近性质.我们还讨论了在多变量随机$F$ -矩阵的背景下进一步的应用。
Generalized Laguerre Unitary Ensembles and an interacting particles model with a wall
我们引入并研究了一个新的相互作用粒子模型，该模型具有一个壁和两种相互作用-阻塞和推动-使粒子保持一定的顺序。我们表明，它涉及一个随机矩阵模型。
Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type particle filters (a.k.a. sequential Monte Carlo), this ensemble-type methodology can also be interpreted as mean-field particle approximations of the Kalman-Bucy filtering equation. In contrast with conventional mean-field type interacting particle methods equipped with a globally Lipschitz interacting drift-type function, Ensemble Kalman filters depend on …
The aim of this paper is to give fine asymptotics for random variables with moments of Gamma type. Among the examples we consider are random determinants of Laguerre and Jacobi beta ensembles with varying dimensions (the number of observed variables and the number of measurements vary and may be different). In addition to the Dyson threefold way of classical random matrix models (GOE, GUE, GSE), we study random determinants of random matrices of the so-called tenfold way, including the Bogoliubov-de Gennes and chiral ensembles from mesoscopic physics. We show that fixed-trace matrix ensembles …
Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles
我们考虑了一些随机对称矩阵的行列式的性质从多元统计发布：Wishart/Laguerre系综（样本协方差矩阵），均匀革兰氏系综（样本相关矩阵）和雅可比系综（MANOVA）。如果$n$是样本的大小，$r\leq n$是变量的数目，$X_{n,r}$是这样一个矩阵，Bartlett型定理的推广给出了$\det X_{n,r}$分解为$r$独立伽玛或贝塔随机变量的乘积。对于固定的$n$，我们研究了$r$增长时的演化，并利用$r/n = t \leq 1$得到了大$r$和$n$的极限。本文给出了{具有独立增量的\it过程}序列$\{n^{-1} \log \det X_{n, \lfloor nt\rfloor}, t \in [0, T]\}_n$对于$T \leq 1$.由于行列式的对数是经验谱分布的线性统计量，我们将边际（固定$t$）的结果与谱方法获得的结果联系起来。实际上，如果我们把行列式定义为电荷的乘积，所有的结果对$β$模型都成立。
Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles
这是“Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles：Announcement of Results”的完整版本，出现在此服务器上，也发表在IMRN 2003，第15号，第15页。821-858.
Geometry of semi-infinite geodesics in the Airy line ensemble
该研究针对Airy线系的半无限测地线，建立了不相交概率、合并深度等的精确估计，刻画了异常行为，确定了两类测地线集合的Hausdorff维数。
Fixed trace $β$-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density
在本文中，固定迹$β$ -Hermite系综推广固定迹高斯Hermite系综。对于所有的$β$，我们用两种不同的方法证明了这些系综的Wigner周期律：一种是借助于一般$β$的矩阵模型的矩等价方法，另一种是利用渐近分析工具.在边缘的密度，我们证明了边缘缩放极限$β$ -HE意味着相同的限制固定的跟踪$β$ -Hermite合奏。因此，可以给出固定迹GOE、GUE和GSE的显式极限。此外，对于甚至$β$，类似于$β$ -Hermite系综，可以获得Konstevich型的多重积分。
We study averages of multiplicative eigenvalue statistics in ensembles of orthogonal Haar distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. We obtain new asymptotics for symbols with Fisher-Hartwig singularities in cases where some of the singularities merge together, and for symbols with a gap or an emerging gap. We obtain these asymptotics by relying on known analogous results in the unitary group and on asymptotics for associated orthogonal polynomials on the unit circle. As consequences of our results, we derive asymptotics for gap probabilities in t…
We consider the Gaussian beta-ensemble when $β$ scales with $n$ the number of particles such that $\displaystyle{{n}^{-1}\ll β\ll 1}$. Under a certain regime for $β$, we show that the largest particle satisfies a large deviations principle in $\mathbb{R}$ with speed $nβ$ and explicit rate function. As a consequence, the largest particle converges in probability to $2$, the rightmost point of the semicircle law.
Central Limit Theorems for Biorthogonal Ensembles and Asymptotics of Recurrence Coefficients
我们研究了某些双正交系综的光滑函数对应的线性统计量的涨落。我们研究了双正交系综的基础双正交家庭满足有限项递归和描述的渐近波动使用的递归矩阵的右极限。因此，我们表明，只要右极限是一个洛朗矩阵，中心极限定理成立。我们还将讨论正交多项式系综的影响。特别地，我们得到了一个中心极限定理的正交多项式系综与任何措施属于Nevai类的一个区间。我们的结果也推广了以前的结果酉系综在一个切割的情况下。最后，我们将说明我们的结果，通过导出的中心极限定理的哈恩系综菱形镶嵌的六边形和厄米特两个矩阵模型。
An asymptotic link between LUE and GUE and its spectral interpretation
我们使用一个矩阵中心极限定理，这使得高斯酉包络出现作为一个限制的拉盖尔酉包络与观察由于约翰森，以获得新的表示GUE的本征值。例如，在某些定向布朗渗流中，可以恢复GUE的最大特征值与最后通过时间之间的著名分布相等。GUE的其他特征值也出现类似的身份。
On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles
本文考虑具有随机独立元素的N维实对称矩阵族H，其方差由函数U（（x-y）/b）确定.在（相对）窄带宽1<<b<<N的极限下，我们显式地得到了H的预解式的1/b-展开式的首项.导出的表达式表明，U（t）的衰减速率决定了本征值相关函数的泛值型的几个尺度。特别地，在U（t）= o（1/t^3）的情况下，得到了具有比率N/b^2的Altshuller-Shklovski渐近性。
Long-time asymptotics for Airy wanderer line ensembles
本文研究了Airy wanderer线集合在长时间行为下的渐进行为，揭示了其在宏观尺度上的结构组织及极限性质。
Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials
本文利用最速下降法研究了一类特征值分布为P_{N}（z_{1}，.的正态随机矩阵系综的积分核z_{N}）= Z_{N} ^{-1} e^{-N <$_{i=1}^{N}V_α（z_{i}）}<$_{1 \leqi <j \leqN }| z_{i} - z_{j}|其中V_α（z）= |z| ^α，z \in C和α \in ]0，\infty [.渐近分析与误差估计。这个扩展的一个推论是一个缩放限制的n点函数的积分核的经典Segal-巴格曼空间。
Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble
考虑来自高斯酉包络（GUE）的$n \times n$矩阵。给定一个有限的集合有界不相交的真正博雷尔集$(Δ_{i,n},\ 1\leq i\leq p)$，适当重新缩放，并最终包括在任何附近的支持维格纳的半圆定律，我们证明了相关的计数措施$({\mathcal N}_n(Δ_{i,n}), 1\leq i\leq p)$，其中${\mathcal N}_n(Δ)$代表的本征值的数量在$Δ$，是渐近独立的大小$n$走向无穷大，$p$被固定。因此，我们证明了最大和最小的特征值，适当的中心和重新缩放，是渐近独立的，我们最后描述的波动的条件数的矩阵从GUE。
We introduce and study stochastic $N$-particle ensembles which are discretizations for general-$β$ log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, $(z,w)$-measures, etc. We prove that under technical assumptions on general analytic potential, the global fluctuations for such ensembles are asymptotically Gaussian as $N\to\infty$. The covariance is universal and coincides with its counterpart in random matrix theory. Our main tool is an appropriate discrete version of the Schwinger-Dyson (or loop) equations, which originates in the work…
Asymptotics for products of characteristic polynomials in classical $β$-Ensembles
研究了$N\times N$随机矩阵的Hermite（Gaussian）、Laguerre（Chiral）和Jacobi $β$ -系综特征值的局部性质.更具体地，我们计算特征多项式的乘积的期望值的缩放极限为$N\to\infty$。在每个$β$系综的大部分频谱中，发现相同的缩放极限是$e^{p_{1}}{}_1F_{1}$，其在杰克多项式方面的精确扩展是众所周知的。Hermite和Laguerre $β$ -系综的软边缘处的标度极限被证明是一个多元Airy函数，它被定义为一个广义Kontsevich积分。作为推论，当$β$是偶数时，得到了三个系综的$k$点关联函数的标度极限。本文还给出了多变量Airy函数在大小变元下的渐近性。所有的渐近结果依赖于推广的沃森引理和Selberg型积分的最速下降法。
Asymptotic Independence of the Extreme Eigenvalues of GUE
我们给出了一个简短的，运营商理论证明的渐近独立性（包括第一个校正项）的最小和最大特征值的n \times n高斯酉Entrance在大矩阵限制n \to \infty。这是通过将极端特征值的联合概率分布表示为渐近变为对角的算子矩阵的弗雷德霍姆行列式来实现的。作为推论，我们得到了极值特征值的相关性渐近地表现为n^{-2/3}/4σ^2，其中σ^2表示Tracy-Widom分布的方差。虽然我们推测Wigner随机埃尔米特矩阵系综的极值特征值是渐近独立的，但相关性的渐近行为中的实际常数是特定的，因此可以用来在统计上区分高斯酉系综与其他Wigner系综。
Invariant $β$-Wishart ensembles, crossover densities and asymptotic corrections to the Marchenko-Pastur law
我们构造了一般连续$β$（或Laguerre）系综的扩散矩阵模型，该模型在正交/酉群变换下保持不变性.用数据矩阵的最大尺寸$M$作为$β=2c/M$（其中$c$是固定的正常数）来缩放Dyson指数$β$，我们得到由$c$参数化的谱密度族。随着$c$的变化，该密度在Mar \vcenko -Pastur（$c\to \infty$限值）和Gamma定律（$c\to 0$限值）之间连续插值。分析完整的Stieltjes变换（预解式）方程，作为副产品，我们获得了对Mar \vcenko -Pastur密度的修正，对于所有$β$，修正到1/M阶，对于特定情况$β=1,2$，修正到$1/M^2$阶。
Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge III: Generating Functions
本文研究了高斯和拉格朗日族在软边缘处的渐近展开，重点分析了间隙概率生成函数的修正项结构及其多项式系数，同时验证了正交和辛族的假设。
Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities
本文研究了高斯和拉盖尔随机矩阵集合在软边缘处的渐近展开，通过斜正交多项式构造得到能级密度的简洁表达式，并用于重建生成函数渐近展开的修正项。
We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer $G$-functions or Wright's generalized Bessel functions. They generalize in a natural way the hard edge Bessel kernel Fredholm determinant. We express the logarithmic derivatives of the Fredholm determinants identically in terms of a $2\times 2$ Riemann-Hilbert problem, and use this repre…
Hard edge asymptotics of correlation functions between singular values and eigenvalues
本文研究双酉不变随机矩阵中特征值与奇异值的$1,k$点相关函数，推导多项式及Pólya系综在硬边缘和Jacobi软-硬边缘的大$n$渐近。
Bulk asymptotics of the Gaussian $β$-ensemble characteristic polynomial
本文研究高斯β系综特征多项式的体渐近性质，给出同时覆盖局部涨落与全局/介观高斯结构的渐近描述，并得到三项重要推论，拓展了随机矩阵理论相关结果。
Real Second Order Freeness and Haar Orthogonal Matrices
证明了Haar分布正交矩阵和独立随机矩阵系综的渐近实二阶自由性。我们的主要结果是：如果我们有两个独立的具有实二阶极限分布的随机矩阵系综，其中一个系综在正交矩阵的共轭下不变，则这两个系综是渐近实二阶自由的.这捕获了Redelmeier [R1，R2]引入的渐近实二阶自由度的已知示例。
Particle Systems with Repulsion Exponent $β$ and Random Matrices
我们考虑一类粒子系统推广的随机矩阵理论的$β$ -合奏。在这些新的合奏中，粒子在接近时会受到$β>0$的排斥，这与$β$合奏中的情况相同。对于大于零的距离，允许相互作用不同于随机本征值。我们发现，本地散装相关的$β$ -合奏，在随机矩阵理论的普遍性，也出现在这些新的合奏。
Real second-order freeness and the asymptotic real second-order freeness of several real matrix ensembles
在二阶非交换概率空间中引入了实二阶自由度。我们证明了在这个定义下，三个真正的模型的随机矩阵，即真正的Ginibre矩阵，高斯正交矩阵，和真正的Wishart矩阵，是渐近二阶自由。这些合奏不满足复杂的定义，满足其复杂的类似物的二阶自由度。我们使用一种组合的方法来矩阵计算类似于复杂的随机矩阵的属扩张，但其中出现了不可定向曲面，展示了真实模型之间的共性和与其复杂类似物的区别，激发了这种独特的定义。在实际情况下，我们发现，除了出现在复杂的情况下，对应于环形辐条图，一组额外的术语对应于环形辐条图，其中两个圈的环是相反的方向，并在其中矩阵转置出现。
We introduce and study a class of discrete particle ensembles that naturally arise in connection with classical random matrix ensembles, log-gases and Jack polynomials. Under technical assumptions on a general analytic potential we prove that the global fluctuations of these ensembles are asymptotically Gaussian with a universal covariance that remarkably differs from its counterpart in random matrix theory. Our main tools are certain novel algebraic identities that we have discovered. They play a role of discrete multi-level analogues of loop equations.
We prove that the fluctuations of mesocopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under an additional assumption on the local regularity of one of the measures). The convergence rate of the recurrence coefficients determines the range of scales on which the limiting fluctuations are identical. Our main tool is an analysis of the Green's function for the associated Jacobi matrices. As a particular consequence we obtain a Central Limit Theorem for…
Asymptotic analysis of the characteristic polynomial for the Elliptic Ginibre Ensemble
本文研究复椭圆 Ginibre 系综，证明其归一化特征多项式在谱椭圆外依分布收敛于高斯解析函数的指数，并借助 Hermite 核控制与矩量法回答可积情形的插值问题。
Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results
我们计算了正交多项式关于有限集上的一般纯点测度的点态渐近性，当测度的节点数和正交多项式的次数都变大时.我们考虑的正交多项式类包括Krawtchouk和Hahn经典离散正交多项式的特殊情况，但更为一般。特别地，我们考虑不一定等距的节点。除了具有任意小但固定半径的圆盘的有限并外，对复平面上的所有点给出了渐近结果和误差界。这些特殊的圆盘是相关的平衡测度的所谓带边的邻域。作为应用，我们证明了一般类离散正交多项式系综的相关函数的普适性结果，特别是我们推导出了具有误差界的渐近公式的某些统计相关的随机平铺六边形菱形瓷砖。离散正交多项式的特点是一个黎曼-希尔伯特问题制定的亚纯矩阵具有一定的极点条件。通过推广[17，22]的方法，我们提出了一种处理黎曼-希尔伯特问题的一般和统一的方法，当未知矩阵的极点在所关心的渐近极限的某个集合上积累时.
Rider, Sinclair and Xu (2013) introduced a solvable two charge ensemble of interacting charged particles on the real line in the presence of the harmonic oscillator potential. It can be seen as a special form of a grand canonical ensemble with the total charge being fixed and unit charge particles being random. Moreover, it serves as an interpolation between the Gaussian orthogonal and the Gaussian symplectic ensembles and maintains the Pfaffian structure of the eigenvalues. A similar solvable ensemble of charged particles on the unit circle was studied by Shum and Sinclair (2014) and Forreste…
Macroscopic asymptotics in discrete beta-ensembles and random tilings
研究离散β集合体的宏观渐近行为，通过分析粒子分布的线性统计和分区函数，揭示随机铺砌和高斯自由场的波动特性。
Let $\mathbf{T}_{d, N}: Ω\to \mathbb{R}^{N^d}$ be a random real symmetric Wigner-type tensor. For unit vectors $(u_N^{(i, j)})_{i \in I, j \in [d-2]} \subset \mathbb{S}^{N-1}$, we study the contracted tensor ensemble \[ \left(\frac{1}{\sqrt{N}}\mathbf{T}_{d, N}\left[u_N^{(i, 1)} \otimes \cdots \otimes u_N^{(i, d-2)}\right]\right)_{i \in I}. \] For large $N$, we show that the joint spectral distribution of this ensemble is well-approximated by a semicircular family $(s_i)_{i \in I}$ whose covariance $(\mathbf{K}_{i, i'}^{(N)})_{i, i'\in I}$ is given by the rescaled overlaps of the corresponding…
A Solvable Two-Charge Ensemble on the Circle
我们引入一个系综，由排斥电荷1和电荷2粒子的单位圆约束，使所有粒子的总电荷等于$N$，但每种粒子的比例允许根据逸度参数变化。我们用$N$确定逸度的适当比例，使每个粒子的比例在$N \rightarrow \infty$极限内保持正值。该系综在单位圆上形成了一个Pfavian点过程，我们导出了矩阵核的尺度极限作为插值参数的函数。这提供了一个可解的圆酉和辛系综之间的插值。
We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C^+ associated with the ax+b (affine) group, depending on an admissible Hardy function ψ. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω contained in C^+. As a special case one recovers the DPP related to the weighted Bergman kernel. When ψ is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau lev…
We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms of either the Hyperpfaffian or the Berezin integral of an appropriate alternating tensor. Adjusting the distances between these lines (or circles) gives an interpolation between a pair of limiting ensembles, such as one-dimensional $β$-ensembles with $β=K$ and $β=K^2$.
Asymptotic expansions for the Gaussian Unitary Ensemble
设g：{ \mathbb R} --> { \mathbb C}是所有导数有界的C^{ \infty }-函数，tr_n表示n × n矩阵上的正规化迹. Ercolani和McLaughlin在文献[EM]中对一类相当一般的随机矩阵X_n，包括高斯酉矩阵（GUE），建立了均值E{tr_n（g（X_n））}的渐近展开。使用分析的方法，我们在本文中提供了一个替代的证明，这种渐近展开的GUE的情况下。具体地，我们推导出对于GUE随机矩阵X_n，E{tr_n（g（X_n））}= \frac{1}{2π} \int_{-2}^2 g（x）\sqrt{4-x^2} dx + \sum_{j=1}^k \frac{α_j(g)}{n^{2j}} + O（n^{-2k-2}），其中k是任意正整数。考虑g的映射，我们确定系数α_j（g），j \in{\mathbb N}为L. Schwarts）。我们得到了协方差Cov{Tr_n[f（X_n）]，Tr_n[g（X_n）]}的一个类似的渐近展开式，其中f是与g同类的函数，Tr_n= ntr_n.特别关注的情况下，g（x）=1/（z-x）和f（x）=1/（w-x）的非实复数z和w。在这种情况下，上面考虑的均值和协方差分别对应于GUE（n，1/n）的一维和二维柯西（或斯蒂尔吉斯）变换。
Asymptotics of the real eigenvalue distribution for the real spherical ensemble
本文研究实球面系综中实特征值数量的概率分布，通过库仑气体和生成函数方法，推导大偏差、中间偏差及局部中心极限区域的渐近行为，并给出无实特征值概率的渐近形式。
Scattering of the Toda system and the Gaussian $β$-ensemble
该研究利用作用于对称实三对角矩阵的经典Toda流，给出了Dumitriu-Edelman三对角模型谱服从高斯β系综的辛证明，拓展了Toda系统散射与对数气体矩阵模型的相关研究。
The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability distribution weighted by an exponential factor whose exponent is uniquely determined by the condition. We apply this theorem to explain the canonical equilibrium ensemble of a system in contact with a heat reservoir. Since the theorem only requires analysis at the level of the function of the subsystem and reservoir, it is applicable even without the knowledge …
A New Look at the Ensemble Kalman Filter for Inverse Problems: Duality, Non-Asymptotic Analysis and Convergence Acceleration
本文通过新的对偶视角，提出改进EnKI算法的收敛策略，加速EnKF在逆问题中的收敛速度并提升解的质量。
Large Deviations for the Bose--Einstein Condensate of the Ideal Gas in the Canonical Ensemble
该研究针对正则系综下受一般单粒子哈密顿量支配的非相互作用玻色气体，得出其玻色-爱因斯坦凝聚体粒子数的大偏差估计，发现左右尾概率随粒子数趋于无穷时以不同指数速率衰减。
We introduce ensembles of repelling charged particles restricted to a ball in a non-archimedean field (such as the $p$-adic numbers) with interaction energy between pairs of particles proportional to the logarithm of the ($p$-adic) distance between them. In the {\em canonical ensemble}, a system of $N$ particles is put in contact with a heat bath at fixed inverse temperature $β$ and energy is allowed to flow between the system and the heat bath. Using standard axioms of statistical physics, the relative density of states is given by the $β$ power of the ($p$-adic) absolute value of the Vanderm…
We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point charge at the origin, we derive the asymptotic behaviour of the correlation kernels both in the macro- and microscopic scales. In the macroscopic scale, this particularly shows that there are strong correlations among the particles on the boundary of the droplets. In the microscopic scale, this establishes the edge universality. For the proofs, we use the nonlinear steepest descent method on the matrix…
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。