arXiv subjects

Peter Major

Publications and source records attributed to Peter Major.

13 recordsLinked to original sources

arXiv2026

Design and performance of the Fast Beam Condition Monitor for luminosity and background measurement at the CMS Experiment in LHC Run 3

The Fast Beam Condition Monitor (BCM1F) has been used at the CMS Experiment since the first LHC circulating beams in 2008. Originally meant as a beam-induced background monitor for fast beam losses detection, it showed a potential also for luminosity measurements in 2012 running, and has been used for luminosity measurements since the beginning of Run 2 data taking in 2015 as a part of the Beam Radiation, Instrumentation and Luminosity (BRIL) system. Over the years, the system has undergone various upgrades to the sensors, the front-end and back-end electronics, providing improvements in the precision of the measurements, that remain valid in the higher pileup conditions of LHC Run 3 (2022-2026). Based on the experience of all BCM1F Run 2 upgrades, the detector was completely rebuilt prior to LHC Run 3 using AC-coupled silicon-pad diodes and active cooling. This latest detector version exhibits excellent linearity with instantaneous luminosity and achieves nanosecond-level timing precision, enabling improved systematic corrections for luminosity and background measurements. This paper presents a detailed overview of the detector system for LHC Run 3, including the selection and qualification of sensors as well as a summary of the readout system. It also outlines the processing and calibration strategy for luminosity data, discussing operational hurdles and comparing BCM1F measurements to other CMS luminosity measurements to assess the system's performance as a luminometer. Lastly, the implications for the design of a future luminosity detector to be used in the envisioned HL-LHC upgrade are discussed.

physics.ins-det↗

arXiv2019

Wiener--Ito integral representation in vector valued Gaussian stationary random fields

The subject of this work is the multivariate generalization of the theory of multiple Wiener--It\^o integrals. In the scalar valued case this theory was described in paper\cite{11}. Our proofs apply the technique of this work, but in the proof of some results new ideas were needed. The motivation for this study was a result in paper\cite{1} of Arcones where he formulated the multivariate version of a non-central limit theorem for non-linear functionals of Gaussian stationary random fields presented in paper\cite{6}. We found the proof in paper\cite{1} incomplete and wanted to give a full proof. We did it in paper\cite{13}, but in that proof we needed a detailed description of the properties of non-linear functionals of vector valued stationary Gaussian fields. Here we provide the foundation needed to carry out that proof. --More--(0%)

math.PR↗

arXiv2019

Non-central limit theorem for non-linear functionals of vector valued Gaussian stationary random fields

Here I prove non-central limit theorems for non-linear functionals of vector valued stationary random fields under appropriate conditions. They are the multivariate versions of the results in paper\cite{2}. Previously A. M. Arcones formulated a theorem in paper\cite{1} which can be considered as the multivariate generalization of these results. But I found Arcones' discussion incomplete, and in my opinion to give a complete proof first a more profound foundation of the theory of vector valued Gaussian stationary random fields has to be worked out. This was done in my paper\cite{4} which enabled me to adapt the method in paper\cite{2} to the study of the vector valued case. Here I prove with its help the desired multivariate version of the results in paper\cite{2}.

math.PR↗

arXiv2017

Limit theorems for non-linear functionals of stationary Gaussian random fields

This is an extended version of a series of talks I held at the University of Bochum in 2017 about limit theorems for non-linear functionals of stationary Gaussian random fields. The goal of these talks was to give a fairly detailed introduction to the theory leading to such results, even if some of the results are presented without proof. On the other hand, I gave a simpler proof for some of the results. (The proofs omitted from this text can be found in my Springer Lecture Note Multiple Wiener--Ito Integrals. In this note first I discuss the spectral representation of the covariance function of a Gaussian stationary rendom field by means of the spectral measure and the representation of the elements of the random field by means of a random integral with respect to the random spectral measure. Then I construct the multiple random integrals with respect to the random spectral measure and prove their most important properties. Finally I show some interesting applications of these multiple random integrals. In particular, I prove some non-trivial non-Gaussian limit theorems

math.PR↗

arXiv2014

Sharp estimate on the supremum of a class of partial sums of small i.i.d. random variables

We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ together with a sequence of independent, identically distributed $X$-space valued random variables $\xi_1,\dots,\xi_n$ and give a good estimate on the tail distribution of $\sup_{f\in\Cal F}\sum_{j=1}^n f(\xi_j)$ if the expected values $E|f(\xi_1)|$ are very small for all $f\in\Cal F$. In a subsequent paper~[2] we shall give a sharp bound for the supremum of normalized sums of i.i.d. random variables in a more general case. But that estimate is a consequence of the results in this work.

math.PR↗

arXiv2014

On the tail behaviour of the distribution function of the maximum for the partial sums of a class of i.i.d. random variables

We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ and a sequence of i.i.d. $X$-valued random variables $\xi_1,\dots,\xi_n$, and give a good estimate on the tail behaviour of $\sup\limits_{f\in\Cal F}\sum\limits_{j=1}^nf(\xi_j)$ if the conditions $\sup\limits_{x\in X}|f(x)|\le1$, $Ef(\xi_1)=0$ and $Ef(\xi_1)^2<\sigma^2$ with some $0\le\sigma\le1$ hold for all $f\in\Cal F$. Roughly speaking this estimate states that under some natural conditions the above considered supremum is not much larger than the worst element taking part in it. The proof heavily depends on the main result of paper~[3]. Here we have to deal with such a problem where the classical methods worked out to investigate the behaviour of Gaussian or almost Gaussian random variables do not work.}

math.PR↗

arXiv2009

Estimates on the tail behavior of Gaussian polynomials. The discussion of a result of Latala

In this paper a result of Latala about the tail behavior of Gaussian polynomials will be discussed. Latala proved an interesting result about this problem in paper [2]. But his proof applied an incorrect statement at a crucial point. Hence the question may arise whether the main result of paper [2] is valid. The goal of this paper is to settle this problem by presenting such a proof where the application of the erroneous statement is avoided. I discuss the proofs in detail even at the price of a longer text and try to give such an explanation that reveals the ideas behind them better than the original paper. \

math.PR↗

arXiv2008

Estimation of Wiener--Ito integrals and polynomials of independent Gaussian random variables

In this paper I prove good estimates on the moments and tail distribution of $k$-fold Wiener--Itô integrals and also present their natural counterpart for polynomials of independent Gaussian random variables. The proof is based on the so-called diagram formula for Wiener--Itô integrals which yields a good representation for their products as a sum of such integrals. I intend to show in a subsequent paper that this method also yields good estimates for degenerate $U$-statistics. The main result of this paper is a generalization of the estimates of Hanson and Wright about bilinear forms of independent standard normal random variables. On the other hand, it is a weaker estimate than the main result of a paper of Latała [6]. But that paper contains an error, and it is not clear whether its result is true. This question is also discussed here.

math.PR↗

arXiv2007

Geometry dependence of the conductance oscillations of monovalent atomic chains

Using a tight binding model we calculate the conductance of monovalent atomic chains for different contact geometries. The leads connected to the chains are modelled as semi-infinite fcc lattices with different orientations and couplings. Our aim is twofold: To check the validity of a three-parametric conductance formula for differently oriented leads, and to investigate the geometry dependence of the conductance oscillations. We show that the character of these oscillations depends strongly on the geometry of the chain-lead coupling.

cond-mat.mes-hall↗

arXiv2005

Tail behaviour of multiple random integrals and U-statistics

This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito integrals with respect to a white noise. It also contains good estimates about the supremum of appropriate classes of such integrals or U-statistics. The proof of most results is omitted, I have concentrated on the explanation of their content and the picture behind them. I also tried to explain the reason for the investigation of such questions. My goal was to yield such a presentation of the results which a non-expert also can understand, and not only on a formal level.

math.PR↗

arXiv2003

An estimate about multiple stochastic integrals with respect to a normalized empirical measure

Let a sequence of iid. random variables $ξ_1,...,ξ_n$ be given on a measurable space $(X,\cal X)$ with distribution $μ$ together with a function $f(x_1,...,x_k)$ on the product space $(X^k,{\cal X}^k)$. Let $μ_n$ denote the empirical measure defined by these random variables and consider the random integral $$ J_{n,k}(f)={n^{k/2}\over{k!}}\int' f(u_1,...,u_k) (μ_n(du_1)-μ(du_1))...(μ_n(du_k)-μ(du_k)), $$ where prime means that the diagonals are omitted from the domain of integration. In this work a good bound is given on the probability $P(|J_{n,k}(f)|>x)$ for all $x>0$. This result shows that the tail behaviour of the distribution funtcion of the random integral $J_{n,k}(f)$ and that of the integral of the function $f$ with respect to a Gaussian random field show a similar behaviour. The proof is based on an adaptation of some methods of the theory of Wiener--Ito integrals. In particular, a sort of diagram formula is proved for the random integrals $J_{n,k}(f)$ together with some of its important properties, a result which may be interesting in itself. The relation of this estimate to some results about $U$-statistics is also discussed.

math.PR↗

arXiv2003

An estimate on the maximum of a nice class of stochastic integrals

Let a sequence of iid. random variables $ξ_1,...,ξ_n$ be given on a space $(X,\cal X)$ with distribution $μ$ together with a nice class $\cal F$ of functions $f(x_1,...,x_k)$ of $k$ variables on the product space $(X^k,{\cal X}^k)$. For all $f\in\cal F$ we consider the random integral $J_{n,k}(f)$ of the function $f$ with respect to the $k$-fold product of the normalized signed measure $\sqrt n(μ_n-μ)$, where $μ_n$ denotes the empirical measure defined by the random variables $ξ_1,...,ξ_n$ and investigate the probabilities $P(\sup_{f\in {\cal F}}|J_{n,k}(f)|>x)$ for all $x>0$. We show that for nice classes of functions, for instance if $\cal F$ is a Vapnik-Cervonenkis class, an almost as good bound can be given for these probabilities as in the case when only the random integral of one function is considered.

math.PR↗

arXiv2002

A Thouless-Like Effect in the Dyson Hierarchical Model with Continuous Symmetry

We study Dyson's classical $r$-component ferromagnetic hierarchical model with a long range interaction potential $U(i,j)= -l(d(i,j)) d^{-2}(i,j)$, where $d(i,j)$ denotes the hierarchical distance. We prove a conjecture of Dyson, which states that the convergence of the series $l_1+l_2+...$, where $l_n=l(2^n)$, is a necessary and sufficient condition of the existence of phase transition in the model under consideration, and the spontaneous magnetization vanishes at the critical point, i.e. there is no Thouless' effect. We find however that the distribution of the normalized average spin at the critical temperature $T_c$ tends to the uniform distribution on the unit sphere in $\Bbb R^r$ as the volume tends to infinity, a phenomenon which resembles the Thouless effect.

math-ph↗