arXiv subjects

Avinash Chand Yadav

Publications and source records attributed to Avinash Chand Yadav.

25 records · Page 2Linked to original sources

arXiv2017

Correspondence between noisy sample space reducing process and records in correlated random events

We study survival time statistics in a noisy sample space reducing (SSR) process. Our simulations suggest that both the mean and standard deviation scale as $\sim N/N^λ$, where $N$ is the system size and $λ$ is a tunable parameter that characterizes the process. The survival time distribution has the form $\mathcal{P}_{N}(τ)\sim N^{-θ}J(τ/N^θ)$, where $J$ is a universal scaling function and $θ= 1-λ$. Analytical insight is provided by a conjecture for the equivalence between the survival time statistics in the noisy SSR process and the record statistics in a correlated time series modeled as drifted random walk with Cauchy distributed jumps.

cond-mat.stat-mech↗

arXiv2016

A general mechanism for the `$1/f$' noise

We consider the response of a memoryless nonlinear device that converts an input signal $ξ(t)$ into an output $η(t)$ that only depends on the value of the input at the same time, $t$. For input Gaussian noise with power spectrum $1/f^α$, the nonlinearity modifies the spectral index of the output to give a spectrum that varies as $1/f^{α'}$ with $α' \neq α$. We show that the value of $α'$ depends on the nonlinear transformation and can be tuned continuously. This provides a general mechanism for the ubiquitous `$1/f$' noise found in nature.

cond-mat.stat-mech↗

arXiv2016

Emergent organization in a model market

We study the collective behavior of interacting agents in a simple model of market economics originally introduced by Nørrelykke and Bak. A general theoretical framework for interacting traders on an arbitrary network is presented, with the interaction consisting of buying (namely, consumption) and selling (namely, production) of commodities. Extremal dynamics is introduced by having the agent with least profit in the market readjust prices, causing the market to self--organize. We study this model market on regular lattices in two--dimension as well as on random complex networks; in the critical state fluctuations in an activity signal exhibit properties that are characteristic of avalanches observed in models of self-organized criticality, and these can be described by power--law distributions.

q-fin.GN↗

arXiv2016

Exact solution for a sample space reducing stochastic process

Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic process that results in a random sequence of strictly decreasing integers $\{x(t)\}$, $0\le t \le τ$, with boundary conditions $x(0) = N$ and $x(τ)$ = 1. This model is shown to be exactly solvable: $\mathcal{P}_N(τ)$, the probability that the process survives for time $τ$ is analytically evaluated. In the limit of large $N$, the asymptotic form of this probability distribution is Gaussian, with mean and variance both varying logarithmically with system size: $\langle τ\rangle \sim \ln N$ and $σ_τ^{2} \sim \ln N$. Correspondence can be made between survival time statistics in the SSR process and record statistics of i.i.d. random variables.

cond-mat.stat-mech↗

arXiv2013

Memoryless nonlinear response: A simple mechanism for the 1/f noise

Discovering the mechanism underlying the ubiquity of $"1/f^α"$ noise has been a long--standing problem. The wide range of systems in which the fluctuations show the implied long--time correlations suggests the existence of some simple and general mechanism that is independent of the details of any specific system. We argue here that a {\it memoryless nonlinear response} suffices to explain the observed non--trivial values of $α$: a random input noisy signal $S(t)$ with a power spectrum varying as $1/f^{α'}$, when fed to an element with such a response function $R$ gives an output $R(S(t))$ that can have a power spectrum $1/f^α$ with $α< α'$. As an illustrative example, we show that an input Brownian noise ($α'=2$) acting on a device with a sigmoidal response function $R(S)= \sgn(S)|S|^x$, with $x<1$, produces an output with $α= 3/2 +x$, for $0 \leq x \leq 1/2$. Our discussion is easily extended to more general types of input noise as well as more general response functions.

cond-mat.stat-mech↗

arXiv2012

Scaling behaviour in probabilistic neuronal cellular automata

We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean--field theory.

cond-mat.stat-mech↗

arXiv2012

Power spectrum of mass and activity fluctuations in a sandpile

We consider a directed abelian sandpile on a strip of size $2\times n$, driven by adding a grain randomly at the left boundary after every $T$ time-steps. We establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeroes in the ternary-base representation of the position of a random walker on a ring of size $3^n$. We find that while the fluctuations of mass have a power spectrum that varies as $1/f$ for frequencies in the range $ 3^{-2n} \ll f \ll 1/T$, the activity fluctuations in the same frequency range have a power spectrum that is linear in $f$.

cond-mat.stat-mech↗