Related papers: Integrable probability: From representation theory…
It is known that solutions of Richardson equations can be represented as stationary points of the "energy" of classical free charges on the plane. We suggest to consider "probabilities" of the system of charges to occupy certain states in…
With the guidance offered by nonequilibrium statistical thermodynamics, simulation techniques are elevated from brute-force computer experiments to systematic tools for extracting complete, redundancy-free and consistent coarse grained…
This mini-review discusses the recent contribution of theoretical and computational physics as well as experimental efforts to the understanding of the behavior of colloidal particles in confined geometries and at liquid crystalline…
Hypothesis: The collective dynamics and self-assembly of colloids floating at a fluid/fluid interface is a balance between deterministic lateral interaction forces, viscous resistance to colloid motion along the surface and thermal…
From first principles, the author gathers a few general rules that need to be abided by in the calculation of the internal partition functions (IPFs) of individual molecules. These rules are violated in many schemes in the literature where…
Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…
We review the literature on the localization transition for the class of polymers with random potentials that goes under the name of copolymers near selective interfaces. We outline the results, sketch some of the proofs and point out the…
We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building Bayesian models of the kinds used in…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influence the…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
This note provides a pedagogical introduction to Langer's theory for activated rate processes in multiple dimensions at the high friction limit, with an emphasis on the connection between the theory and the property of the backward…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
Let k be an algebraically closed field of characteristic p>0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions…
We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…
We establish a relation between the approximation in $L^2[-\pi,\pi]$ by exponentials with the set of frequencies of Beurling--Malliavin density less than $1$ and the meromorphic interpolation at $\mathbb Z$. Furthermore, we show that…
We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
We use the class of commuting quantum computations known as IQP (Instantaneous Quantum Polynomial time) to strengthen the conjecture that quantum computers are hard to simulate classically. We show that, if either of two plausible…