arXiv subjects

Raghavendra Tripathi

Publications and source records attributed to Raghavendra Tripathi.

22 records · Page 2Linked to original sources

arXiv2023

Central limit theorem in complete feedback games

Consider a well-shuffled deck of cards of $n$ different types where each type occurs $m$ times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is removed from the deck. The total number of correct guesses in a complete feedback game has attracted significant interest in last few decades. Under different regimes of $m, n$, the expected number of correct guesses, under the greedy (optimal) strategy, has been obtained by various authors, while there are not many results available about the fluctuations. In this paper, we establish a central limit theorem with Berry-Esseen bounds when $m$ is fixed and $n$ is large. Our results extend to the case of decks where different types may have different multiplicity, under suitable assumptions.

math.PR↗

arXiv2023

Gradient flows on graphons: existence, convergence, continuity equations

Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction involving a gradient-type potential. However, in many problems, such as in multi-layer neural networks, the so-called particles are edge weights on large graphs whose nodes are exchangeable. Such large graphs are known to converge to continuum limits called graphons as their size grow to infinity. We show that the Euclidean gradient flow of a suitable function of the edge-weights converges to a novel continuum limit given by a curve on the space of graphons that can be appropriately described as a gradient flow or, more technically, a curve of maximal slope. Several natural functions on graphons, such as homomorphism functions and the scalar entropy, are covered by our set-up, and the examples have been worked out in detail.

math.PR↗

arXiv2021

Finding Structure in Sequences of Real Numbers via Graph Theory: a Problem List

We investigate a method of generating a graph $G=(V,E)$ out of an ordered list of $n$ distinct real numbers $a_1, \dots, a_n$. These graphs can be used to test for the presence of interesting structure in the sequence. We describe sequences exhibiting intricate hidden structure that was discovered this way. Our list includes sequences of Deutsch, Erdős, Freud & Hegyvari, Recaman, Quet, Zabolotskiy and Zizka. Since our observations are mostly empirical, each sequence in the list is an open problem.

math.CO↗

arXiv2020

Determinantal Processes and Stochastic Domination

We prove the stochastic domination for determinantal processes associated with finite rank projection kernels. The result was first proved by Lyons in discrete setting. We avoid the machinery of matroids in order to obtain a proof that works in a general setting. We prove another result on the stochastic domination of two determinantal processes where the kernels are represented with respect to different measures. Combining this result with Lyons' theorem on the Stochastic domination we obtain a result on the stochastic domination for the last passage time in a directed last passage percolation on $\mathbb{Z}^2$ with i.i.d. geometric weights.

math.PR↗