Related papers: Precise Deviations for the Ewens-Pitman Model

We report a numerical study of the bond-diluted 2-dimensional Potts model using transfer matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in…

This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…

We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…

We study the spectrum of phase transitions with prescribed mean curvature in Riemannian manifolds. These phase transitions are solutions to an inhomogeneous semilinear elliptic PDE that give rise to diffuse objects (varifolds) that limit to…

In this paper, a novel Koopman-type inverse operator for linear time-invariant non-minimum phase systems with stochastic disturbances is proposed. This operator employs functions of the desired output to directly calculate the input.…

We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…

We study moderate deviations in the exponential corner growth model, both in the bulk setting and the increment-stationary setting. The main results are sharp right-tail bounds on the last-passage time and the exit point of the…

Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…

Let $Z_1, \cdots, Z_n$ denote the eigenvalues of the product $\prod_{j=1}^{k_n} \boldsymbol{A}_j$, where $\{\boldsymbol{A}_j\}_{1 \le j \le k_n}$ are independent $n\times n$ complex Ginibre matrices. Define $\alpha = \lim\limits_{n \to…

Consider a random permutation of $\{1, \ldots, \lfloor n^{t_2}\rfloor\}$ drawn according to the Ewens measure with parameter $t_1$ and let $K(n, t)$ denote the number of its cycles, where $t\equiv (t_1, t_2)\in\mathbb [0, 1]^2$. Next,…

Usually Fokker-Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we…

We study the critical properties of the Lipkin-Meshkov-Glick Model in terms of the fidelity susceptibility. By using the Holstein-Primakoff transformation, we obtain explicitly the critical exponent of the fidelity susceptibility around the…

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…

The extraordinary transition which occurs in the two-dimensional O(n) model for $n<1$ at sufficiently enhanced surface couplings is studied by conformal perturbation theory about infinite coupling and by finite-size scaling of the spectrum…

We consider the O(n) loop model on tetravalent maps and show how to rephrase it into a model of bipartite maps without loops. This follows from a combinatorial decomposition that consists in cutting the O(n) model configurations along their…

In the present paper the phase transition in the regularized U(1) gauge theory is investigated using the dual Abelian Higgs model of scalar monopoles. The corresponding renormalization group improved effective potential, analogous to the…

The asymptotic analysis of a linear high-field Wigner-BGK equation is developped by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number $\epsilon$, evolution equations are…

We revisit the scaling properties of a model for non-equilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special…

This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…

Motivated by metastability in the zero-range process, we consider i.i.d.\ random variables with values in $\N_0$ and Weibull-like (stretched exponential) law $\mathbb P(X_i =k) = c \exp( - k^\alpha)$, $\alpha \in (0,1)$. We condition on…