Related papers: Sojourn times for Brownian sheet
Experimental verification of the theoretical predictions made by Albert Einstein in his paper, published in 1905, on the molecular mechanisms of Brownian motion established the existence of atoms. In the last 100 years discoveries of many…
The current status of Doubly Special Relativity research program is shortly presented. I dedicate this paper to my teacher and friend Professor Jerzy Lukierski on occasion of his seventieth birthday.
Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook,…
In this contribution we will discuss how the study of various fluctuation observables may be used to explore the phase diagram of the strong interaction. We will briefly summarize the present study of experimental and theoretical research…
This note celebrates the centenary of Jagadis Chandra Bose's classic monograph entitled "Researches on irritability of plants".
A recent essay [1] reminds us of how richly Boltzmann deserves to be admiringly commemorated for the originality of his ideas on the occasion of his 150th birthday. Without any doubt, the scientific community owes Boltzmann a great debt of…
We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Ito's excursion theory, the pieces between cutpoints form a Poisson process with…
We study the density of the time average of the Brownian meander/excursion over the time interval [0,1]. Moreover we give an expression for the Brownian meander/excursion conditioned to have a fixed time average.
The bijectivity of the mapping, which is represented as expectation, from a family of Gaussian measures parametrized by linear combinations of Dirac measures to the space of classical reflectionless potentials is shown. It is also shown…
This essay is a tribute to Professor Roman Jackiw on the occasion of his eightieth year. It discusses some ideas about Fermion zero modes and fractional charges and quantum entanglement.
We describe the size of the sets of sojourn times $E_\gamma =\{t\geq 0: |B_t|\leq t^\gamma\}$ associated with a fractional Brownian motion $B$ in terms of various large scale dimensions.
This article is a collection of several memories for a special issue of SIGMA devoted to Dmitry Borisovich Fuchs.
In this note we show how to rederive the $A_2$ Rogers-Ramanujan identities proven by Andrews, Schilling and Warnaar using cylindric partitions. This paper is dedicated to George Andrews for his $80^{th}$ birthday.
We can view Brownian sheet as a sequence of interacting Brownian motions or slices. Here we present a number of results about the slices of the sheet. A common feature of our results is that they exhibit phase transition. In addition, a…
This review is an elaboration of a presentation given at the Real algebraic geometry and singularities conference in honor of Wojciech Kucharz's 70th birthday in Krakow in 2022.
Dedicated to George E. Andrews on the occasion of his 70th birthday. Submitted to a special issue for this occasion. We use Andrews' notion of a `signed partition' (i.e. partition where some parts are allowed to be negative) to interpret…
The paper dedicated to memory of Valery Anatolievich Senderov
We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not…
In memory of the famous physicist Bruno Pontecorvo, whereof is just occurred the centenary anniversary of the birth and the twentieth anniversary of the death, this paper traces the scientific and human adventure of the italian scientist,…
Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study the scaling limits of a random…