相关论文: Universal interface width distributions at the dep…
Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…
Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models…
We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponents on the details of the distribution of the noise. All…
Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution and a suitable Gaussian process. Our explicit inequalities…
We study numerically the distribution of zero crossings in one-dimensional elastic interfaces described by an overdamped Langevin dynamics with periodic boundary conditions. We model the %restoring elastic forces with a Riesz-Feller…
The reduced tension $\sigma_{cd}$ of the interface between the confined and the deconfined phase of $SU(3)$ pure gauge theory is determined from numerical simulations of the first transfer matrix eigenvalues. At $T_c = 1/L_t$ we find…
We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1…
We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal…
We revisit the problem of bounding the expected supremum of a canonical Gaussian process indexed by a convex set $T \subset \mathbf{R}^d$. We develop two decompositions for the Gaussian width, based on the geometry of the index set. The…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
We present numerical evidence that there are two distinct universality classes characterizing driven interface roughening in the presence of quenched disorder. The evidence is based on the behavior of $\lambda$, the coefficient of the…
The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity $v$, which increases as $v \sim (F-F_c)^\theta$ for…
We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…
We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely…
The recently introduced framework of universal inference provides a new approach to constructing hypothesis tests and confidence regions that are valid in finite samples and do not rely on any specific regularity assumptions on the…
We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with…
We consider interpolation learning in high-dimensional linear regression with Gaussian data, and prove a generic uniform convergence guarantee on the generalization error of interpolators in an arbitrary hypothesis class in terms of the…