Topic
Ergodic process
About: Ergodic process is a research topic. Over the lifetime, 337 publications have been published within this topic receiving 7432 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: It is shown that an ergodic and a nonergodic process coexist in the plasma membrane and that when the cell is treated with drugs that inhibit actin polymerization, the diffusion pattern of Kv2.1 channels recovers ergodicity.
Abstract: Diffusion in the plasma membrane of living cells is often found to display anomalous dynamics. However, the mechanism underlying this diffusion pattern remains highly controversial. Here, we study the physical mechanism underlying Kv2.1 potassium channel anomalous dynamics using single-molecule tracking. Our analysis includes both time series of individual trajectories and ensemble averages. We show that an ergodic and a nonergodic process coexist in the plasma membrane. The ergodic process resembles a fractal structure with its origin in macromolecular crowding in the cell membrane. The nonergodic process is found to be regulated by transient binding to the actin cytoskeleton and can be accurately modeled by a continuous-time random walk. When the cell is treated with drugs that inhibit actin polymerization, the diffusion pattern of Kv2.1 channels recovers ergodicity. However, the fractal structure that induces anomalous diffusion remains unaltered. These results have direct implications on the regulation of membrane receptor trafficking and signaling.
714 citations
1 Jan 1975
TL;DR: In this article, the authors studied the integrability of nonlinear wave equations with constant coefficients on the torus, and the existence of heteroclinic orbits, with applications to the hopf bifurcation problem.
Abstract: Time evolution of large classical systems.- Ergodic properties of infinite systems.- Time evolution and ergodic properties of harmonic systems.- The laser: A reversible quantum dynamical system with irreversible classical macroscopic motion.- What does it mean for a mechanical system to be isomorphic to the Bernoulli flow?.- The Geodesic flow on surfaces of negative curvature.- Lectures on the billiard.- Spectral invariants and smooth ergodic theory.- Nonlinear wave equations.- Integrable systems of nonlinear evolution equations.- Discrete and periodic illustrations of some aspects of the inverse method.- Finitely many mass points on the line under the influence of an exponential potential -- an integrable system.- On traveling wave solutions of nonlinear diffusion equations.- The existence of heteroclinic orbits, and applications.- Hadamard's generalization of hyperbolicity, with applications to the hopf bifurcation problem.- Hyperbolic sets and shift automorhpisms.- Triple collision in Newtonian gravitational systems.- Solutions of the collinear four body problem which become unbounded in finite time.- On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus.
471 citations
TL;DR: Deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games are provided, and probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow are provided.
Abstract: This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the discrete stochastic process, for large populations, and its deterministic flow approximation. In particular, we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow. We sharpen these results in the special case of ergodic processes.
369 citations
TL;DR: In this paper, strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds are established for linear and some nonlinear processes, and strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.
Abstract: We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.
246 citations
TL;DR: Positive association between the number of transactions and the volatility process of a certain stock is discovered and it is proved that the maximum likelihood estimator of the vector of unknown parameters is asymptotically normal with a covariance matrix that can be consistently estimated.
241 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 7 |
| 2019 | 12 |
| 2018 | 6 |
| 2017 | 7 |
| 2016 | 14 |