Related papers: New Instantons for Matrix Models
A path integral over trajectories of $2n$ fluid particles is identified with a $2n$-th order correlation function of a passive scalar convected by $d$-dimensional short-correlated multi-scale incompressible random velocity flow. Strong…
The Stokes multipliers in the matrix models are invariants in the string-theory moduli space and related to the D-instanton chemical potentials. They not only represent non-perturbative information but also play an important role in…
Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…
We develop a Gaussian process regression enhanced line integral string method to accelerate ring polymer instanton calculations of tunneling rates and tunneling splittings in molecular proton transfer reactions. By exploiting uncertainty…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
The role of instantons in describing non-perturbative aspects of globally supersymmetric gauge theories is reviewed. The cases of theories with N=1, N=2 and N=4 supersymmetry are discussed. Special attention is devoted to the intriguing…
We provide asymptotic theory for certain functions of the sample autocovariance matrices of a high-dimensional time series with infinite fourth moment. The time series exhibits linear dependence across the coordinates and through time.…
Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to computing thermal reaction rates for complex molecular systems including quantum tunneling effects. There have been a number of attempts to…
We study the effect of D-instantons on closed string scattering amplitudes in the two-dimensional type 0B string theory from the worldsheet perspective. We find that the contribution from a pair of D-instanton and anti-D-instanton to the…
This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex…
The eigenvalues of the transmission matrix provide the basis for a full description of the statistics of steady-state transmission and conductance. At the same time, the ability to excite the sample with the waveform of specific…
We present a new way to compute and interpret quantum tunneling in a 1-D double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been…
We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We introduce templates for exponential asymptotic expansions that, in contrast to matched asymptotic approaches, enable the simultaneous satisfaction of both boundary values in classes of linear and nonlinear equations that are singularly…
We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials and one interval limiting spectrum. Our starting point is the result of \cite{S:08} on the representation of the…
In the study of quantum-mechanical tunneling processes, numerous approaches have been developed to determine the decay rate of states initially confined within a metastable potential region. Virtually all analytical treatments, however,…
This work addresses nonperturbative effects in both matrix models and topological strings, and their relation with the large-order behavior of the 1/N expansion. We study instanton configurations in generic one-cut matrix models, obtaining…