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In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed…
A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within…
People counting system in crowded places has become a very useful practical application that can be accomplished in various ways which include many traditional methods using sensors. Examining the case of real time scenarios, the algorithm…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
Markets efficiency implies that the stock returns are intrinsically unpredictable, a property that makes markets comparable to random number generators. We present a novel methodology to investigate ultra-high frequency financial data and…
Modern high-energy physics experiments collect data using dedicated complex multi-level trigger systems which perform an online selection of potentially interesting events. In general, this selection suffers from inefficiencies. A further…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
Information flow analysis has largely ignored the setting where the analyst has neither control over nor a complete model of the analyzed system. We formalize such limited information flow analyses and study an instance of it: detecting the…
We introduce an optimization technique to discriminate signal and background in any phenomeno- logical study based on the cut and count-based method. The core ideas behind this technique are the introduction of a ranking scheme that can…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…
It is generally assumed that every process in quantum physics can be described mathematically by a completely positive map. However, experimentally reconstructed processes are not necessarily completely positive due to statistical or…
We propose and analyze a protocol to study quantum information scrambling using statistical correlations between measurements, which are performed after evolving a quantum system from randomized initial states. We prove that the resulting…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
Many physicists think that the maximum entropy formalism is a straightforward application of Bayesian statistical ideas to statistical mechanics. Some even say that statistical mechanics is just the general Bayesian logic of inductive…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
The validity of various bootstrapping methods has been proved for the sample mean of strongly mixing data. But in many applications, there appear nonlinear statistics of processes that are not strongly mixing. We investigate the…