Related papers: Oded Schramm's contributions to noise sensitivity
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in…
Phase noise correction is crucial to exploit full advantage of orthogonal frequency division multiplexing (OFDM) in modern high-data-rate communications. OFDM channel estimation with simultaneous phase noise compensation has therefore drawn…
Fluctuations play a central role in many fields of physics, from quantum electrodynamics to statistical mechanics. In active matter physics, most models focus on thermal fluctuations due to a surrounding solvent. An alternative but much…
In the past two decades or so, we have learned how to understand crackling noise in a wide variety of systems. We review here the basic ideas and methods we use to understand crackling noise - critical phenomena, universality, the…
The non-random fluctuation is one of the central objects in first passage percolation. It was proved in [Shuta Nakajima. Divergence of non-random fluctuation in First Passage Percolation. {\em Electron. Commun. Probab.} 24 (65), 1-13.…
This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6.…
Transformer-based pretrained language models (PLMs) have achieved great success in modern NLP. An important advantage of PLMs is good out-of-distribution (OOD) robustness. Recently, diffusion models have attracted a lot of work to apply…
We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
Noise measurement is a powerful tool to investigate many phenomena from laser characterization to quantum behavior of light. In this paper, we report on intensity noise measurements obtained when a laser beam is transmitted through a large…
Orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has recently emerged as a promising paradigm for ensuring reliable communications in doubly-selective channels. This work investigates the spectra and orthogonality…
We study the relationship between dynamical properties and interaction patterns in complex oscillator networks in the presence of noise. A striking finding is that noise leads to a general, one-to-one correspondence between the dynamical…
Sensitivity to initial conditions in the coherent noise model of biological evolution, introduced by Newman, is studied by making use of damage spreading technique. A power-law behavior has been observed, the associated exponent $\alpha$…
This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…
In the colour string model the impact of string percolation on multiplicities, their long-range correlations and average transverse momentum is studied. The multiplicities are shown to be damped by a simple factor which follows from the…
We prove that for Bernoulli percolation on $\mathbb{Z}^d$, $d\geq 2$, the percolation density is an analytic function of the parameter in the supercritical interval. For this we introduce some techniques that have further implications. In…
Lidar SLAM plays a significant role in mobile robot navigation and high-definition map construction. However, existing methods often face a trade-off between localization accuracy and system robustness in scenarios with a high proportion of…
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise - that is, we modulate…
Theory of spin noise in low dimensional systems and bulk semiconductors is reviewed. Spin noise is usually detected by optical means, continuously measuring the rotation angle of the polarization plane of the probe beam passing through the…