VKVladislav Kargin
Vladislav Kargin
*This is an algorithmically generated author record based on publicly available information.
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Vladislav Kargin has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Alexei Onatski
University of Cambridge
2 shared publications - Gérard Ben Arous
Courant Institute of Mathematical Sciences, New York University, New York, USA
2 shared publications Yinsong Chen
Binghamton Univ, Dept Math & Stat, Binghamton, NY 13850 USA
2 shared publications- Yinsong Chen
Department of Mathematics and Statistics Binghamton University Binghamton New York U.S.A
2 shared publications - Simon R. Blackburn
Dept. of Mathematics, Royal Holloway, University of London, Egham, Surrey, United Kingdom
1 shared publication
Latest Publications
- Open Access
- 27 August 2026
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 39 (4) , 70
Free Compressions of R-Diagonal Random Variables and the Semigroup of Brown Measures
We investigate the Brown measures of compressions of $$ R $$ -diagonal random variables, extending previous results to include unbounded cases. For random variables with finite variance, we demonstrate that the Brown measures of their compressions converge to the uniform distribution on the unit disk. In the case of infinite variance, we characterize the Brown measures that remain stable under the compression operation and explore their properties in detail.- 27 August 2026
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 39 (4) , 70
Open AccessFree Compressions of R-Diagonal Random Variables and the Semigroup of Brown Measures
We investigate the Brown measures of compressions of $$ R $$ -diagonal random variables, extending previous results to include unbounded cases. For random variables with finite variance, we demonstrate that the Brown measures of their compressions converge to the uniform distribution on the unit disk. In the case of infinite variance, we characterize the Brown measures that remain stable under the compression operation and explore their properties in detail. - 1 January 2026
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 31 (none) , 1-30
The smallest singular value of large random rectangular Toeplitz and circulant matrices
Let {xi}i∈Z be a sequence of i.i.d. standard normal random variables. We consider two classes of rectangular random matrices: Toeplitz X=(xj−i)1≤i≤p,1≤j≤n and circulant X=(x(j−i)modn)1≤i≤p,1≤j≤n. We let p,n→∞ so that p∕n→c∈(0,1]. Our main result is that, for any c∈(0,1], the smallest eigenvalue of 1nXX⊤ converges to zero both in probability and in expectation. We further establish a lower bound on the rate of this convergence, showing it is faster than any poly-logarithmic rate yet slower than any polynomial rate. In the “rectangular circulant” setting, we additionally derive a simple, explicit upper bound on the convergence rate in terms of c. This upper bound implies that, for sufficiently small c, the decay of the smallest eigenvalue to zero can be made arbitrarily slow on a polynomial scale.
- 1 January 2026
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 31 (none) , 1-30
The smallest singular value of large random rectangular Toeplitz and circulant matrices
Let {xi}i∈Z be a sequence of i.i.d. standard normal random variables. We consider two classes of rectangular random matrices: Toeplitz X=(xj−i)1≤i≤p,1≤j≤n and circulant X=(x(j−i)modn)1≤i≤p,1≤j≤n. We let p,n→∞ so that p∕n→c∈(0,1]. Our main result is that, for any c∈(0,1], the smallest eigenvalue of 1nXX⊤ converges to zero both in probability and in expectation. We further establish a lower bound on the rate of this convergence, showing it is faster than any poly-logarithmic rate yet slower than any polynomial rate. In the “rectangular circulant” setting, we additionally derive a simple, explicit upper bound on the convergence rate in terms of c. This upper bound implies that, for sufficiently small c, the decay of the smallest eigenvalue to zero can be made arbitrarily slow on a polynomial scale.
- Open Access
- 12 September 2025
- Published by California Digital Library (CDL) in Combinatorial Theory
- Vol. 5 (3)
An upper bound on the per-tile entropy of ribbon tilings
This paper considers \(n\)-ribbon tilings of general regions and their per-tile entropy (the binary logarithm of the number of tilings divided by the number of tiles). We show that the per-tile entropy is bounded above by \(\log_2 n\). This bound improves the best previously known bounds of \(n-1\) for general regions, and the asymptotic upper bound of \(\log_2 (en)\) for growing rectangles, due to Chen and Kargin.Mathematics Subject Classifications: 05B45, 52C20Keywords: Ribbon tilings, domino tilings, dimer tilings- 12 September 2025
- Published by California Digital Library (CDL) in Combinatorial Theory
- Vol. 5 (3)
Open AccessAn upper bound on the per-tile entropy of ribbon tilings
This paper considers \(n\)-ribbon tilings of general regions and their per-tile entropy (the binary logarithm of the number of tilings divided by the number of tiles). We show that the per-tile entropy is bounded above by \(\log_2 n\). This bound improves the best previously known bounds of \(n-1\) for general regions, and the asymptotic upper bound of \(\log_2 (en)\) for growing rectangles, due to Chen and Kargin.Mathematics Subject Classifications: 05B45, 52C20Keywords: Ribbon tilings, domino tilings, dimer tilings - Open Access
On the joint distribution of the area and the number of peaks for Bernoulli excursions
Let $P_n$ be a random Bernoulli excursion of length $2n$. We show that the area under $P_n$ and the number of peaks of $P_n$ are asymptotically independent. We also show that these statistics have the correlation coefficient asymptotic to $c /\sqrt{n}$ for large $n$, where $c < 0$, and explicitly compute the coefficient $c$.Open AccessOn the joint distribution of the area and the number of peaks for Bernoulli excursions
Let $P_n$ be a random Bernoulli excursion of length $2n$. We show that the area under $P_n$ and the number of peaks of $P_n$ are asymptotically independent. We also show that these statistics have the correlation coefficient asymptotic to $c /\sqrt{n}$ for large $n$, where $c < 0$, and explicitly compute the coefficient $c$. - Open Access
Scaling limits of slim and fat trees
We consider Galton--Watson trees conditioned on both the total number of vertices $n$ and the number of leaves $k$. The focus is on the case in which both $k$ and $n$ grow to infinity and $k = \alpha n + O(1)$, with $\alpha \in (0, 1)$. Assuming the exponential decay of the offspring distribution, we show that the rescaled random tree converges in distribution to Aldous' Continuum Random Tree with respect to the Gromov--Hausdorff topology. The scaling depends on a parameter $\sigma^\ast$ which we calculate explicitly. Additionally, we compute the limit for the degree sequences of these random trees.Open AccessScaling limits of slim and fat trees
We consider Galton--Watson trees conditioned on both the total number of vertices $n$ and the number of leaves $k$. The focus is on the case in which both $k$ and $n$ grow to infinity and $k = \alpha n + O(1)$, with $\alpha \in (0, 1)$. Assuming the exponential decay of the offspring distribution, we show that the rescaled random tree converges in distribution to Aldous' Continuum Random Tree with respect to the Gromov--Hausdorff topology. The scaling depends on a parameter $\sigma^\ast$ which we calculate explicitly. Additionally, we compute the limit for the degree sequences of these random trees. - 18 July 2023
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 340, 85-103
The number of ribbon tilings for strips
- 18 July 2023
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 340, 85-103
The number of ribbon tilings for strips
- Open Access
The Number of Ribbon Tilings for Strips
First, we consider order-$n$ ribbon tilings of an $M$-by-$N$ rectangle $R_{M,N}$ where $M$ and $N$ are much larger than $n$. We prove the existence of the growth rate $γ_n$ of the number of tilings and show that $γ_n \leq (n-1) \ln 2$. Then, we study a rectangle $R_{M,N}$ with fixed width $M=n$, called a strip. We derive lower and upper bounds on the growth rate $μ_n$ for strips as $ \ln n - 1 + o(1) \leq μ_n \leq \ln n $. Besides, we construct a recursive system which enables us to enumerate the order-$n$ ribbon tilings of a strip for all $n \leq 8$ and calculate the corresponding generating functions.Open AccessThe Number of Ribbon Tilings for Strips
First, we consider order-$n$ ribbon tilings of an $M$-by-$N$ rectangle $R_{M,N}$ where $M$ and $N$ are much larger than $n$. We prove the existence of the growth rate $γ_n$ of the number of tilings and show that $γ_n \leq (n-1) \ln 2$. Then, we study a rectangle $R_{M,N}$ with fixed width $M=n$, called a strip. We derive lower and upper bounds on the growth rate $μ_n$ for strips as $ \ln n - 1 + o(1) \leq μ_n \leq \ln n $. Besides, we construct a recursive system which enables us to enumerate the order-$n$ ribbon tilings of a strip for all $n \leq 8$ and calculate the corresponding generating functions. - 23 June 2023
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 36 (4) , 2192-2228
Scaling Limits of Slim and Fat Trees
- 23 June 2023
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 36 (4) , 2192-2228
Scaling Limits of Slim and Fat Trees
- Open Access
- 7 April 2023
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 30 (2) , P2.15
On Enumeration and Entropy of Ribbon Tilings
The paper considers ribbon tilings of large regions and their per-tile entropy (the logarithm of the number of tilings divided by the number of tiles). For tilings of general regions by tiles of length $n$, we give an upper bound on the per-tile entropy as $n - 1$. For growing rectangular regions, we prove the existence of the asymptotic per tile entropy and show that it is bounded from below by $\log_2 (n/e)$ and from above by $\log_2(en)$. For growing generalized "Aztec Diamond" regions and for growing "stair" regions, the asymptotic per-tile entropy is calculated exactly as $1/2$ and $\log_2(n + 1) - 1$, respectively.- 7 April 2023
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 30 (2) , P2.15
Open AccessOn Enumeration and Entropy of Ribbon Tilings
The paper considers ribbon tilings of large regions and their per-tile entropy (the logarithm of the number of tilings divided by the number of tiles). For tilings of general regions by tiles of length $n$, we give an upper bound on the per-tile entropy as $n - 1$. For growing rectangular regions, we prove the existence of the asymptotic per tile entropy and show that it is bounded from below by $\log_2 (n/e)$ and from above by $\log_2(en)$. For growing generalized "Aztec Diamond" regions and for growing "stair" regions, the asymptotic per-tile entropy is calculated exactly as $1/2$ and $\log_2(n + 1) - 1$, respectively. - 9 November 2020
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 181 (6) , 2322-2345
Cycles in Random Meander Systems
- 9 November 2020
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 181 (6) , 2322-2345
Cycles in Random Meander Systems