相关论文: Zeev Schuss' legacy: an unexpected path in applied…

Automated interpretability research has recently attracted attention as a potential research direction that could scale explanations of neural network behavior to large models. Existing automated circuit discovery work applies activation…

Nonequilibrium statistical physics is concerned with a fundamental problem in physics, the phenomenon of irreversibility, which is not rigorously solved yet. Different approaches to the statistical mechanics of nonequilibrium processes are…

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting $K$-matrices leading to four different types of…

We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002)…

The algebraic and combinatorial theory of shuffles, introduced by Chen and Ree, is further developed and applied to the study of multiple zeta values. In particular, we establish evaluations for certain sums of cyclically generated multiple…

Schubert polynomials were discovered by A. Lascoux and M. Sch\"utzenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials. In…

Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…

This paper examines Schwarzschild's key contributions to general relativity through his two papers. It focuses on his method for developing exterior and interior solutions. The study emphasizes Schwarzschild's ingenious methods and the…

Motivated by the probabilistic methods for nonlinear differential equations introduced by McKean (1975) for the Kolmogorov-Petrovski-Piskunov (KPP) equation, and by Le Jan and Sznitman (1997) for the incompressible Navier-Stokes equations,…

In 1963 [Ann. of Math. {\bf 78}, 267-288], Gerstenhaber invented a \emph{comp(osition)} calculus in the Hochschild complex of an associative algebra. In this paper, the first steps of the Gerstenhaber theory are exposed in an abstract (comp…

In this work, we establish a general relationship between the enumeration of weighted directed paths and skew Schur functions, extending work by Bousquet-M\'elou, who expressed generating functions of discrete excursions in terms of…

We provide multiple Schramm-Loewner evolutions (SLEs) to describe the scaling limit of multiple interfaces in critical lattice models possessing Lie algebra symmetries. The critical behavior of the models is described by Wess-Zumino-Witten…

This note provides a chronological account of Fr\'echet distances, starting with Maurice Fr\'echet's 1906 doctoral thesis on distances in abstract sets and tracing the Fr\'echet distance between polygonal curves and its algorithmic…

The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a…

We study rare transitions in Markovian open quantum systems driven with Gaussian noise, applying transition path and interface sampling methods to trajectories generated by stochastic Schr\"odinger dynamics. Interface and path sampling…

In this article algorithmic methods are presented that have essentially been introduced into computer algebra systems like Mathematica within the last decade. The main ideas are due to Stanley and Zeilberger. Some of them had already been…

The theory of discrete stochastic systems has been initiated by the work of Shannon and von Neumann. While Shannon has considered memory-less communication channels and their generalization by introducing states, von Neumann has studied the…

Gerhard Hochschild's contribution to the development of mathematics in the XX century is succinctly surveyed. We start with a personal and mathematical biography, and then consider with certain detail his contributions to algebraic groups…

Inspired by the recent 90th anniversary of the Scottish Book we present some reflections about its impact. First we discuss new areas of mathematics it helped launch. Then we argue that it was actively used in stimulating the interests and…

We construct discrete time Markov chains that preserve the class of Schur processes on partitions and signatures. One application is a simple exact sampling algorithm for q^{volume}-distributed skew plane partitions with an arbitrary back…