Related papers: Entropy-controlled Last-Passage Percolation
This paper presents a unified exposition of rough path methods applied to optimal control, robust filtering, and optimal stopping, addressing a notable gap in the existing literature where no single treatment covers all three areas. By…
Temporal correlation for randomly growing interfaces in the KPZ universality class is a topic of recent interest. Most of the works so far have been concentrated on the zero temperature model of exponential last passage percolation, and…
We investigate the impact of an external pressure on the structure of self-gravitating polytropes for axially symmetric ellipsoids and rings. The confinement of the fluid by photons is accounted for through a boundary condition on the…
The pseudo entropy is a promising recent generalization of the entanglement entropy to the situations in which both the initial and final state are involved, with the density matrix promoted to the transition matrix. However, in contrast to…
We begin with an exact expression for the entropy of a system of hard spheres within the Hamming space. This entropy relies on probability marginals, which are determined by an extended set of Belief Propagation (BP) equations. The BP…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $\mathbb{Z}^d$, $d\geq 3$, the FPP distance is comparable to the graph distance with high…
The objective of this paper is to develop a duality between a novel Entropy Martingale Optimal Transport problem (A) and an associated optimization problem (B). In (A) we follow the approach taken in the Entropy Optimal Transport (EOT)…
Entropic Optimal Transport (EOT), also referred to as the Schr\"odinger problem, seeks to find a random processes with prescribed initial/final marginals and with minimal relative entropy with respect to a reference measure. The relative…
Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually defined through the use of some classical losses from…
Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken…
We investigate the entanglement entropy of a two-dimensional disordered system holographically. In particular, we study the evolution of the entanglement entropy along renormalization group flows for a conformal theory at the UV fixed…
We consider a nonlocal analogue of the Fisher-KPP equation. We do not assume that the Borel-measure for the convolution is absolutely continuous. In order to show the main result, we modify a recursive method for abstract monotone discrete…
Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting…
The state space of our model is the Euclidean space in dimension d = 2. Simultaneously, from all points of a homogeneous Poisson point process, we let grow independent and identically distributed random continuum paths. Each path stops…
Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for…
The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms…
In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary…
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on $\mathbb Z^d$ ($d\geq 2$). The models under interest include classical Bernoulli bond and site percolation…
We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…