Theoretical Statistics and Mathematics Unit

## All upcoming Seminars and Colloquia

### BANGALORE PROBABILITY SEMINAR

Title : Statistical analysis of associated data using U-statistics
Speaker : Mansi Garg (Indian Statistical Institute)
Time : January 22, 2018 (Monday), 02:15 PM
Venue : Auditorium
Abstract : A notion of positive dependence between random variables is association. Associated random variables often occur in models based on monotonic transformations and hence several applications can be found in reliability and survival analysis. In this talk, we discuss the limiting behavior of U-statistics based on associated random variables. We present results on asymptotic normality of U-statistics and discuss consistent estimators of the limiting variance of U-statistics. We also discuss bootstrap of the sample mean for functions of associated random variables and for U-statistics based on associated random variables. Finally, as applications, we look into tests for exponentiality against positive ageing and a test for change in mean, when the underlying sample consists of functions of associated random variables.

### BANGALORE PROBABILITY SEMINAR

Title : Holder exponents for Loewner traces
Speaker : Atul Shekhar (KTH Stochholm)
Time : January 22, 2018 (Monday), 03:30 PM
Venue : Auditorium
Abstract : We consider planar curves arising from solving Loewner differential equation driven by 1/2-Holder real valued functions. We will look at the problem of understanding the distance of the curve from the hyperbolic boundary of the domain containing it. We will derive conclusions about the regularity of the curve from above. We also make comparison to previously known results when the driver is the Brownian motion. The talk will be based on an ongoing joint work with Fredrik Viklund and Lukas Schoug.

### STUDENT SEMINAR

Title : The contradictions of neoliberalism - Interpreting India's banking crisis
Speaker : C P Chandrasekhar (Center For Economic Studies and Planning JNU)
Time : January 23, 2018 (Tuesday), 03:15 PM
Venue : Auditorium

### COLLOQUIUM

Title :Translation Invariant Diffusions
Speaker : B. Rajeev (ISI Bangalore)
Time : January 25, 2018 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : In this talk we will discuss the existence and uniqueness of a class of stochastic partial differential equations (SPDE) that generalize the classical Ito stochastic differential equations and also the SPDE in Rajeev (2013, IJPAM). We will discuss some applications and (time permitting) give an idea of the proofs of existence and uniqueness.

### COLLOQUIUM

Title :Pair correlation for Hecke eigenvalues
Speaker : Kaneenika Sinha (IISER Pune)
Time : February 12, 2018 (Monday), 02:00 PM
Venue : Auditorium
Abstract : Distribution of prime numbers is among the most important themes in mathematics. In the last few decades, this theme has evolved into fine questions about spacing between consecutive prime numbers. Such questions can be generalised to the values at prime numbers of important arithmetic functions. After a historical overview of such questions, we consider the spacing statistics for eigenvalues of Hecke operators $T_p$ ($p$ denotes a prime) acting on spaces of modular cusp forms with prescribed weights and levels. This is a report on joint work with Baskar Balasubramanyam.

### BANGALORE PROBABILITY SEMINAR

Title : A probabilistic approach to Voronin's universality theorem.
Speaker : Bhaskar Bagchi (Indian Statistical Institute Bangalore)
Time : February 12, 2018 (Monday), 03:30 PM
Venue : Auditorium
Abstract : The universality theorem on the Riemann Zeta function states that any non-vanishing holomorphic function on the strip 1/2 < Re(z) < 1 can be arbitrarily well approximated (in the topology of locally uniform convergence) by vertical translates of Zeta. In this talk I intend to discuss the probabilistic approach to this theorem given in my Ph.D. thesis. This approach actually proves a very much stronger version of the universality theorem.

### COLLOQUIUM

Title :An invariance principle for sums and record times of regularly varying stationary sequences
Speaker : Philippe Soulier (University Paris Nanterre)
Time : February 15, 2018 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of point process convergence theorem. It is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling. This allows to prove a new functional limit theorem. Its assumptions are satisfied by a wide class of applied time series models, for which standard limiting theory in the space D of cadlag functions does not apply. We further apply our method to analyze record times in a sequence of dependent stationary observations, even when their marginal distribution is not necessarily regularly varying. Under certain restrictions on dependence among the observations, we show that the record times after scaling converge to a relatively simple compound scale invariant Poisson process. Joint work with Bojan Basrak and Hrvoje Planinic (both in Zagreb University).

### STUDENT SEMINAR

Title : Exciting Physics Inspired by Nature: Flocking and Bacterial Heat Engine
Speaker : Ajay K Sood (President - Indian National Science Academy; Indian Institute of Science)
Time : March 27, 2018 (Tuesday), 03:15 PM
Venue : Platinum Jubliee Auditorium
Abstract : This talk will bring out how nature inspires us to explore fascinating phenomena like flocking, a self-organized motion of vast numbers individuals of same species in same direction. It is a common behavior seen in many animals like ants, locusts, birds, fishes etc. As a physicist, I along with my colleagues have tried to understand this beautiful phenomenon in the laboratory by working with inanimate polar granular objects made active by placing them on rapidly vibrating surface amongst spherical beads[1]. The conventional macroscopic heat engine, a device to convert thermal energy to mechanical energy, is a triumph of our understanding of classical thermodynamics over the last three centuries. In recent years, taking the heat engine concepts to microscopic scale, necessarily dominated by fluctuations, has led to the development of stochastic thermodynamics. We have shown that a micrometer-sized active Stirling engine can be realized by periodically cycling a colloidal particle in a time-varying harmonic optical potential across bacterial baths at different activities[2]. Our experiments bring out a message towards the fundamental insights into the functioning of engines operating out of equilibrium.

[Seminar] [Past Seminar] [Stat Math Unit] [Indian Statistical Institute]